A Big Picture Look At “Earth’s Temperature” – Santer 17 Update

The simulations rule out (at the 95% level) zero trends for intervals of 15 yr or more, suggesting that an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate.

Because of the pronounced effect of interannual noise on decadal trends, a multi-model ensemble of anthropogenically-forced simulations displays many 10-year periods with little warming. A single decade of observational TLT data is therefore inadequate for identifying a slowly evolving anthropogenic warming signal. Our results show that temperature records of at least 17 years in length are required for identifying human effects on global-mean tropospheric temperature.

In October 2013, the Remote Sensing Systems (RSS) satellite temperature data set reached a period of 204 months/17 years for which the slope is = -0.000122111 per year. For those not familiar, the RSS satellite temperature data set is similar to the University of Alabama – Huntsville (UAH) dataset that John Christy and Roy Spencer manage. Information about RSS can be found at here and the data set can be found here.
In November 2013, Dr. Robert G. Brown, Physics Department of Duke University wrote on WUWT:

This (17 years) is a non-event, just as 15 and 16 years were non-events. Non-events do not make headlines. Other non-events of the year are one of the fewest numbers of tornadoes* (especially when corrected for under-reporting in the radar-free past) in at least the recent past (if not the remote past), the lowest number of Atlantic hurricanes* since I was 2 years old (I’m 58), the continuation of the longest stretch in recorded history without a category 3 or higher hurricane making landfall in the US (in fact, I don’t recall there being a category 3 hurricane in the North Atlantic this year, although one of the ones that spun out far from land might have gotten there for a few hours). * Links added subsequently

While I must disagree with Dr. Robert G. Brown as to what one can and can’t be make into a headline, I do otherwise agree wholeheartedly. Unfortunately, with mainstream media outlets like PBS are running erroneous headlines like, “UN Panel: ‘Extremely Likely’ Earth’s Rapid Warming Is Caused by Humans” we are stuck reporting on average climate data. Amusingly, it has proven a quite effective method of informing the public and disprove erroneous alarmist claims and headlines, as Dr. Brown’s comment above attests.

For those not too familiar with the “Pause” in Earth’s warming, recommended reading includes: “Over the past 15 years air temperatures at the Earth’s surface have been flat while greenhouse-gas emissions have continued to soar.” The Economist “Global warming stopped 16 years ago, reveals Met Office report quietly released… and here is the chart to prove it.” Daily Mail “Twenty-year hiatus in rising temperatures has climate scientists puzzled.” The Australian “Has the rise in temperatures ‘paused’?” Guardian “On Tuesday, news finally broke of a revised Met Office ‘decadal forecast’, which not only acknowledges the pause, but predicts it will continue at least until 2017.” Daily Mail “RSS global satellite temperatures confirm hiatus of global warming, while the general public and mainstream press are now recognizing the AWOL truth that skeptics long ago identified…global temperatures are trending towards cooling, not accelerating higher” C3 Headlines

1. For GISS, the slope is flat since September 1, 2001 or 12 years, 1 month. (goes to September 30, 2013)
2. For Hadcrut3, the slope is flat since May 1997 or 16 years, 5 months. (goes to September)
3. For a combination of GISS, Hadcrut3, UAH and RSS, the slope is flat since December 2000 or 12 years, 10 months. (goes to September)
4. For Hadcrut4, the slope is flat since December 2000 or 12 years, 10 months. (goes to September)
5. For Hadsst3, the slope is flat since November 2000 or 12 years, 11 months. (goes to September)
6. For UAH, the slope is flat since January 2005 or 8 years, 9 months. (goes to September using version 5.5)
7. For RSS, the slope is flat since November 1996 or 17 years (goes to October)

Here’s what that looks like graphically;

WoodForTrees.org – Paul Clark – Click the pic to view at source

However, to really see the big picture on “Earth’s Temperature” we must take into account many more measurements than just Surface and Tropospheric Temperatures. As such, the following is an overview of many of them. NASA’s Earth Observatory claims that;

“Global warming is the unusually rapid increase in Earth’s average surface temperature over the past century primarily due to the greenhouse gases released by people burning fossil fuels.”

The world added roughly 100 billion tonnes of carbon to the atmosphere between 2000 and 2010. That is about a quarter of all the CO₂ put there by humanity since 1750. And yet, as James Hansen, the head of NASA’s Goddard Institute for Space Studies, observes, “the five-year mean global temperature has been flat for a decade.”

Additionally, surface temperature records are burdened with issues of questionable siting, changes in siting, changes in equipment, changes in the number of measurement locations, modeling to fill in gaps in measurement locations, corrections to account for missing, erroneous or biased measurements, land use changes, anthropogenic waste heat and the urban heat island effect. Thus to see the Big Picture of “Earth’s Temperature”, it also helps to look up.

Atmospheric Temperatures:

Since 1979 Earth’s “temperature” has also been measured via satellite. “The temperature measurements from space are verified by two direct and independent methods. The first involves actual in-situ measurements of the lower atmosphere made by balloon-borne observations around the world. The second uses intercalibration and comparison among identical experiments on different orbiting platforms. The result is that the satellite temperature measurements are accurate to within three one-hundredths of a degree Centigrade (0.03 C) when compared to ground-launched balloons taking measurements of the same region of the atmosphere at the same time.” NASA

According to Remote Sensing Systems, “For Channel (TLT) (Lower Troposphere) and Channel (TMT) (Middle Troposphere), the anomaly time series is dominated by ENSO events and slow tropospheric warming. The three primary El Niños during the past 20 years are clearly evident as peaks in the time series occurring during 1982-83, 1987-88, and 1997-98, with the most recent one being the largest.” RSS

Middle Tropospheric temperatures appear to show slow warming overlaid with the El Niño/La Niña Southern Oscillation (ENSO) cycle, including several comparatively large El Niño events. Middle Tropospheric temperatures appear to entered The Pause with the large El Niño in 1998.

has been in The Pause since records began in 1987, with a trend of just -.004 K/C per decade.

The 1997-98 and 2009 – 10 El Niño events are still readily apparent in the Troposphere / Stratosphere plot above, as is a spike from the 1991 eruption of Mt. Pinatubo. Note that the effect of Mt. Pinatubo is the opposite in the Lower and Middle Troposphere versus the Troposphere / Stratosphere (TTS), i.e. “Large volcanic eruptions inject sulfur gases into the stratosphere; the gases convert into submicron particles (aerosol) with an e-folding time scale of about 1 year. The climate response to large eruptions (in historical times) lasts for several (2-3) years. The aerosol cloud causes cooling at the Earth’s surface, warming in stratosphere.”Ellen Thomas, PHD Wesleyan University

It is interesting that, incorporating the impact of three significant surface driven warming events, Troposphere / Stratosphere Temperatures (TTS) have been quite stable, however there is a bit of regional variation here, e.g.:

The eruptions of El Chichon and Mt Pinatubo are readily apparent in the Apparent Atmospheric Transmission of Solar Radiation at Mauna Loa, Hawaii:

National Oceanic and Atmospheric Administration (NOAA) – Earth System Research Laboratory (ESRL) – Click the pic to view at source

“The stratosphere” … “in contrast to the troposphere, is heated, as the result of near infrared absorption of solar energy at the top of the aerosol cloud, and increased infra-red absorption of long-wave radiation from the Earth’s surface.”

“The stratospheric warming in the region of the stratospheric cloud increases the latitudinal temperature gradient after an eruption at low latitudes, disturbing the stratospheric-troposphere circulation, increasing the difference in height of the troposphere between high and low latitudes, and increasing the strength of the jet stream (polar vortex, especially in the northern hemisphere). This leads to warming during the northern hemisphere winter following a tropical eruption, and this warming effect tends to be larger than the cooling effect described above.” Ellen Thomas, PHD Wesleyan University

The Lower Stratosphere experienced “dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991).” RSS “The long-term, global-mean cooling of the lower stratosphere stems from two downward steps in temperature, both of which are coincident with the cessation of transient warming after the volcanic eruptions of El Chichon and Mt. Pinatubo.” … “Here we provide observational analyses that yield new insight into three key aspects of recent stratospheric climate change. First, we provide evidence that the unusual step-like behavior of global-mean stratospheric temperatures is dependent not only upon the trend but also on the temporal variability in global-mean ozone immediately following volcanic eruptions. Second, we argue that the warming/cooling pattern in global-mean temperatures following major volcanic eruptions is consistent with the competing radiative and chemical effects of volcanic eruptions on stratospheric temperature and ozone. Third, we reveal the contrasting latitudinal structures of recent stratospheric temperature and ozone trends are consistent with large-scale increases in the stratospheric overturning Brewer-Dobson circulation” David W. J. Thompson Colorado State University

Above the Stratosphere we have the Mesosphere and Thermosphere, neither of which have I identified current temperature time series for, but of note is that on “July 15, 2010″ “A Puzzling Collapse of Earth’s Upper Atmosphere” occurred when “high above Earth’s surface where the atmosphere meets space, a rarefied layer of gas called “the thermosphere” recently collapsed and now is rebounding again.”

“This is the biggest contraction of the thermosphere in at least 43 years,” says John Emmert of the Naval Research Lab, lead author of a paper announcing the finding in the June 19th issue of the Geophysical Research Letters (GRL). “It’s a Space Age record.”

The collapse happened during the deep solar minimum of 2008-2009—a fact which comes as little surprise to researchers. The thermosphere always cools and contracts when solar activity is low. In this case, however, the magnitude of the collapse was two to three times greater than low solar activity could explain.

“Something is going on that we do not understand,” says Emmert.

The thermosphere ranges in altitude from 90 km to 600+ km. It is a realm of meteors, auroras and satellites, which skim through the thermosphere as they circle Earth. It is also where solar radiation makes first contact with our planet. The thermosphere intercepts extreme ultraviolet (EUV) photons from the sun before they can reach the ground. When solar activity is high, solar EUV warms the thermosphere, causing it to puff up like a marshmallow held over a camp fire. (This heating can raise temperatures as high as 1400 K—hence the name thermosphere.) When solar activity is low, the opposite happens.”NASA

In summary, “the Pause” is apparent in Earth’s atmospheric record, Lower and Middle Troposphere appear to have warmed slowly, overlaid with the El Niño/La Niña Southern Oscillation (ENSO) cycle, including four comparatively large El Niño events, and tempered by the cooling effects of the eruption of El Chichon (1982) and Mt Pinatubo (1991). Lower and Middle Tropospheric temperatures appear to have paused since the large El Niño in 1998. Tropospheric / Stratospheric temperatures appear to have been influenced by at least three significant surface driven warming events, the 1997-98 El Niño, and the eruptions of El Chichon in 1982 and Mt Pinatubo in 1991, but have maintained a stable overall trajectory. Stratospheric temperatures appear to have experienced two “dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991).”, and “unusual step-like behavior of global-mean stratospheric temperatures” which has resulted in a significant stratospheric cooling during the last 30 years. Lastly, “during deep solar minimum of 2008-2009″ “the biggest contraction of the thermosphere in at least 43 years” occurred and “The magnitude of the collapse was two to three times greater than low solar activity could explain.”

climate4you.com – Ole Humlum – Professor, University of Oslo Department of Geosciences – Click the pic to view at source

It seems apparent from the plots above that Global Ocean Heat has increased over the last several decades, and has not paused per se, however the rate of increase seems to have slowed significantly since 2004.

Sea Level:

“Global sea level is currently rising as a result of both ocean thermal expansion and glacier melt, with each accounting for about half of the observed sea level rise, and each caused by recent increases in global mean temperature. For the period 1961-2003, the observed sea level rise due to thermal expansion was 0.42 millimeters per year and 0.69 millimeters per year due to total glacier melt (small glaciers, ice caps, ice sheets) (IPCC 2007). Between 1993 and 2003, the contribution to sea level rise increased for both sources to 1.60 millimeters per year and 1.19 millimeters per year respectively (IPCC 2007).” Source NSIDC

Global Mean Sea Level Change – 1993 to Present:

climate4you.com – Ole Humlum – Professor, University of Oslo Department of Geosciences – Click the pic to view at source

it is important to note that Sea Levels were increasing at a similar pace during the first half of the 20th century, before anthropogenic CO2 emissions were sufficient to have a significant influence on “Earth’s Temperature” and Sea Level:

Snow and Ice:

A proxy often cited when measuring “Earth’s Temperature” is amount of Snow and Ice on Earth. According to the United States Geological Survey (USGS), “The vast majority, almost 90 percent, of Earth’s ice mass is in Antarctica, while the Greenland ice cap contains 10 percent of the total global ice mass.” Source USGA

However, there is currently no generally accepted measure of ice volume, as Cryosat is still in validation and the accuracy of measurements from Grace are still being challenged. Sea Ice Area and Extent are cited as proxies for “Earth’s Temperature”, however there is significant evidence that the primary influences on Sea Ice Area and Extent are in fact wind and Atmospheric Oscillations.

With this said, Global Sea Ice Area;

Cryosphere Today – University of Illinois – Polar Research Group – Click the pic to view at source

had it’s largest maximum in 2013, since 1996 and has remained stubbornly average for the entirety of 2013. Antarctic Sea Ice Extent has remained above the 1981 – 2010 “normal” range for much of the last four months;

we had the third most expansive Southern Sea Ice Area measured to date;

Cryosphere Today – Arctic Climate Research at the University of Illinois – Click the pic to view at source

and Southern Sea Ice Area has remained above average for almost all of the last two years:

Cryosphere Today – Arctic Climate Research at the University of Illinois – Click the pic to view at source

At the other pole Arctic Sea Ice Extent has remained within the 1981 – 2010 “normal” range for the entirety of 2013;

National Snow & Ice Data Center (NSIDC) – click to view at source

and Northern Hemisphere Sea Ice Area had it’s smallest decline since 2006:

Cryosphere Today – University of Illinois – Polar Research Group – Click the pic to view at source

There appears to have been a negative trend in Northern Hemisphere Sea Ice Area and Extent, a positive trend in Southern Hemisphere Sea Ice Area and Extent, thus the resultant Global Sea Ice Area trend appears to be slightly negative. However, in the last 6 years there does appear to be a Pause in Global Sea Ice Area.

In terms of land based data, here is 20 Year Northern Hemisphere Snow Cover with 1995 – 2009 Climatology from NCEP/NCAR;

Florida State University – Department of Earth, Ocean, and Atmospheric Science – Click the pic to view at source

While none of the Snow plots offers a global perspective, when looking at the Northern Hemisphere, there appears to have been a slight increase in Winter Snowcover and Snow Extent, a decrease in Spring Snow Extent and no change in Fall Snow Extent over the historical record.

Based on the limited Global Ice and Snow measurements available, and noting the questionable value of Sea Ice Area and Extent as a proxy for temperature, not much inference can currently be drawn from Earth’s Ice and Snow measurements. However, there does appear to be a Pause in Global Sea Ice Area.

Conclusion:

The Pause in “Earth’s Temperature” appears in many of Earth’s observational records, it appears to extend for between 6 – 16 years depending on the data set and what it is being measured.

Please note that WUWT cannot vouch for the accuracy of the data/graphics within this article, nor influence the format or form of any of the graphics, as they are all linked from third party sources and WUWT is simply an aggregator. You can view each graphic at its source by simply clicking on it.

Another way they move the goal posts is to allege that areas where temperature is not measured is where all the heat is going. First there was the deep oceans (it magically transported itself below the upper layers) and the latest is that the heat is where the thermometers are not.

Even if they started measuring today, nothing could be determined for 30 years. So their claims cannot be disproven. But neither can they be proven. They are basically unsupported conjecture.

Outstanding!!!
I was just looking this minute for some of these graphs to debunk the propaganda headlines that have been showing up in the MSM. These are so good, I think I will send them to some of my Liberal friends as well. Nothing like a few facts to get the Liberal heads spinning.

You’ve shown TTS (Trop/Strat) and TLS (Lower Strat) plots. The first show mixed results, the latter cooling. But a cooling stratosphere has always been part of AGW theory. In recent years, ozone depletion has caused more cooling than the GHE.

Says AR3:“WMO (1999) concluded, on the basis of intercomparisons of the temperature records as measured by different instruments, that there has been a distinct cooling of the global mean temperature of the lower stratosphere over the past two decades, with a value of about 0.5°C/decade. Model simulations from GCMs using the observed O3 losses yield global mean temperature changes that are approximately consistent with the observations. Such a cooling is also much larger than that due to the well-mixed greenhouse gases taken together over the same time period.”

1. he assumed that the noise structure of GCM is a suitable proxy for the real noise.
its not. especially when Santer included GCMs that dont simulate volcanos
2. he assumed a constant warming signal that has to emerge from the noise.
A) he selected a too warm signal
B) his noise was too benign.
3. he picked a confidence level (95%) that is too low for robust results.

50% of the global warming is hiding in the very deep ocean and other 50% is hiding the arctic where we can’t accurately measure temperature. A nuclear blast is going off every second in the deep ocean releasing global warming it’s just too deep for you to feel it. But you should be alarmed. It’s also just too cold in the arctic for the thermometers to work well so we have to estimate warming because it’s too cold up to live except for Santa Claus, his elves, polar bears and the “deniers’ that sabotage the thermometers. Finally, just because the ground temperature warming is not statistically significant doesn’t mean its not warming. They wouldn’t spend millions our dollars and many hours teaching our children about global warming if it wasn’t really happening. A proper STEM education is too important to our countries future to play politics.

The data you show for 60N to 82.5N for RSS Northern Polar Temperature Lower Troposphere (TLT) Brightness Temperature Anomaly gives a trend of 0.33 C/decade. UAH is probably about the same. This is five times too small to support the claims in the Cowtan and Way paper.
The Arctic covers 4% of the globe surface. To change the 15 year increase from 0.08 C (HadCRUT4) to 0.18 C in the hybrid dataset requires adding in a temperature change of (0.18-0.08)/0.04 = 2.5 C, or 1.67C/decade in the Arctic.

I watched “Question time” last night on TV where Lord Lawson was a panel guest, and the inevitable question was “does the hurricane in the Philippines show the reality of climate change?”
Lawson responded by explaining that there has been no warming in 15 years, and this was met by mocking laughter from other panellists. It is obvious that they thought this was the pronouncements of a deluded fool.

Such a level of ignorance must be difficult to acquire, and the knee jerk response from the shrieky woman who happens to be a member of parliament made me shudder to think that our futures are literally in the hands of people whose cognitive grasp of reality is barely more than that of an adolescent.

Besides the May, 5th 2011, “Glacial Isostatic Adjustment (GIA)” of 0.3 mm/year there have been additional corrections totaling up to 0.6 mm/yr added to the chart put out by Colorado University’s Sea Level Research Group. Remove corrections and sea level for the last ten years has probably gone up at a rate of less than 2 mm/yr

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That graph seems to imply that the CO2 from the steak I grilled last year is still up there mixing with the CO2 from the steam engines from the railroads my great uncles worked for.
Do they tag each molecule?
Do they have some type of “carbon tracing”?

For those who deny the temperature standstill read the many temperature standstill quotes from the climate scientists. The first one is Dr. Phil Jones who reported slight cooling in 2005 and in 2009 said in the CRU emails:

‘Bottom line: the ‘no upward trend’ has to continue for a total of 15 years before we get worried.’

What is significant about 15 years? Why would Phil Jones think 15 years is significant enough to warrant worry? The leaked/hacked CRU emails hold the key to the CAGW scare for they are revealing. I wish some journalist with balls would ask Phil why 15 years of no warming is significant?

Wow! This is a really solid compendium of the temperature data for land, sea and air over the reliably measured time frame. Combined with the sea level data, polar ice data, and snow and ice extents, it paints an increasingly clear and detailed picture of a planet that is no longer warming, even as the inaccurately labeled ‘green house gasses’ have continued their steady rise.

Another WUWT article for reference and wide distribution! Thanks a bunch, JTF!
MtK

1. he assumed that the noise structure of GCM is a suitable proxy for the real noise.
its not. especially when Santer included GCMs that dont simulate volcanos
2. he assumed a constant warming signal that has to emerge from the noise.
A) he selected a too warm signal
B) his noise was too benign.
3. he picked a confidence level (95%) that is too low for robust results.

Warmists seem to be like our Mayor Ford here in Toronto: they can’t quit, but they have no moral standing either. Unfortunately, wonderful posts like this are no more than a punch to the nose of one of those stand-up clown punching bags…

rather the cooling appears to have occurred two steps after the "dramatic warming events caused by the eruptions of El Chichon (1982) and Mt Pinatubo (1991)";RSS. The impact of El Chichon and Mt Pinatubo can be seen in impact seen in Apparent Atmospheric Transmission of Solar Radiation at Mauna Loa, Hawaii:

National Oceanic and Atmospheric Administration (NOAA) – Earth System Research Laboratory (ESRL) – Click the pic to view at source

In recent years, ozone depletion has caused more cooling than the GHE.

justthefactswuwt: “Can you present evidence in support of this statement?”

Hrm.. Off to a bad start. “Do you have any evidence that the previously wrong predictions, that have been shown to be wrong, or not wrong because they quite wrongly looked at the wrong things.”

That’s a game you don’t win. Once Stokes has exhibited the ability to see on which side of a foot, the mark lies, and call it honestly what it is, then *and only then* let him launch into a tirade about how we should in the future change the length of a foot and pretend it always applied to past measurements.

In recent years, ozone depletion has caused more cooling than the GHE.

==========================================================
I read that and couldn’t help but think of Al Gore. He “warned” us about the depleting ozone and the ozone “hole” and then he “warned” us about CO2 emissions and Global Warming.
Will he ever get it right?

Steven Mosher says:
November 15, 2013 at 12:11 pm
santer didnt move the goal posts.
jones was referring to SAT.
Santer is referring to TLT.
Both used different methods to determine an acceptable pause.
Neither method is correct.
I’ll deal with santer
1. he assumed that the noise structure of GCM is a suitable proxy for the real noise.
its not. especially when Santer included GCMs that dont simulate volcanos
2. he assumed a constant warming signal that has to emerge from the noise.
A) he selected a too warm signal
B) his noise was too benign.
3. he picked a confidence level (95%) that is too low for robust results.
________________________________________________________________________
I’m confused. Two world class expert climate scientists, using the methods that make them world class expert climate scientists come up with different time scales for pauses that are significant. The times for significance are passed and they are both wrong? Was this pointed out and hotly debated when they came up with the times? Did they retract and modify? It turns out that Santer’s methodology was suspect in developing his 17 years. If he got that wrong, what else has his methodology missed?
I’ve spent decades developing processes and models that are expected to be correct and work. When they don’t, it gets expensive and getting mulligans has been painful. It seems that the mulligans for AGW are heat hiding in the ocean or where Arctic temperature monitors aren’t. The AGW predictions have been extremely costly and when the leading lights of climate science get it wrong, the mulligans ought to be more than, oops, they were wrong.

All right, I’ll bite. How many years of data do you think are necessary to identify anthropogenic effects on “Earth’s Temperature”? How many years of flat temperatures do you think are necessary before we can state with a reasonable degree of confidence that anthropogenic CO2 is not causing rapid, accelerating, runaway, extreme, catastrophic global warming?

justthefactswuwt says: November 15, 2013 at 12:58 pm
“did not occur in correlation with increasing anthropogenic CO2 emissions”
Well, as I said, ozone depletion was the main factor. But GHG’s were expected to have a cooling effect too. And it cooled.

‘In recent years, ozone depletion has caused more cooling than the GHE.’
“Can you present evidence in support of this statement?”

Besides the May, 5th 2011, “Glacial Isostatic Adjustment (GIA)” of 0.3 mm/year there have been additional corrections totaling up to 0.6 mm/yr added to the chart put out by Colorado University’s Sea Level Research Group. Remove corrections and sea level for the last ten years has probably gone up at a rate of less than 2 mm/yr

Nick Stokes: “Well, as I said, ozone depletion was the main factor. But GHG’s were expected to have a cooling effect too. And it cooled.”

So you’re stating that GHG’s neither have a warming effect nor a cooling effect, and that the AGW hypothesis is falsified? Or did you mean that GHG’s have both a warming effect and a cooling effect and so there is no null hypothesis, or no manner in which to reject one for AGW?

Because both are absurd. But in the latter case it means that AGW is, by your claims, off in the merry myth land with Jesus riding Velociraptors. That is: It doesn’t even pass the smell test for a hypothesis, let alone belong anywhere in science.

OCEANS:
The oceans have been warming for a long time it seems. Three questions. How much warming does measurement create? How do you identify natural from human input? What are the human inputs – sailing, waste disposal, submarines, atomic testing, floating bottles, plastic and other detrus, ships, ad infinitum and maybe, just maybe, a little warming from CO2 (though I don’t know how that would work – can someone explain?) Not sarcasm, actually serious questions from someone who doesn’t understand all the science.

The really big mystery is that the RSS stratosphere data are also dead flat since the mid-1990s. A simple interpretation would be that something is interfering with IR absorption in the troposphere, but what that might be, I have not a clue.

The minim time period required for ‘proof ‘or ‘disprove ‘ of the cause is directly related to if it does the first or the second . If it the first , then any value is good enough , while if its the second than the time scale can never be achieved because gets extended if the condition is meet..

The lower stratosphere has cooled by a globally averaged 0.3–0.5 K decade since 1979 (Ramaswamy et al. 2001; Baldwin et al. 2007, chapter 5; Randel et al. 2009). The global-mean cooling has not occurred monotonically but, rather, is manifested as two downward ‘‘steps’’ in temperature, both of which are coincident with the cessation of transient warming after the major volcanic eruptions of El Chichón and Mount Pinatubo (Pawson et al. 1998; Seidel and Lanzante 2004; Ramaswamy et al. 2006). The lower stratosphere has not noticeably cooled since 1995, which indicates that the trends in this region are not dominantly controlled by the known increases in carbon dioxide over this period (Ramaswamy et al. 2006)

The resulting analyses reveal that the distinct drops in global-mean stratospheric temperatures following the transient warming due to the eruptions of El Chichón and Mount Pinatubo are linearly consistent with concurrent drops in ozone. We note that the several-year
period after the eruption of Mount Pinatubo is unique in the global ozone record, insofar as it is the only period in which concurrent ozone decreases are observed across, not only the tropics and NH midlatitudes, but also SH midlatitudes. The analyses further suggest that the weak rise in global-mean temperatures between the eruption of El Chichón and Mount Pinatubo is consistent with the concomitant weak rise in ozone, and the results clarify that the seemingly mysterious rise in global-mean stratospheric temperatures since 1993 is consistent with increasing stratospheric ozone juxtaposed on global-mean cooling of 0.1 K decade.

Hence, while the solar cycle and variability in upwelling longwave radiation play a role in the time history of global-mean temperatures in recent simulations (e.g., Dameris et al. 2005; Ramaswamy et al. 2006), our analyses suggests that neither factor is necessary to explain the steplike variability that dominates the observed record of T. We argue that the pattern of rising
and lowering temperatures following the eruptions of El Chichón and Mount Pinatubo is consistent with the competing radiative and chemical effects of volcanic eruptions on stratospheric climate.

@Wayne: Warming from measurement isn’t really a factor as such. More properly, any immediate excess heat as part of the measurement process can create bad readings. But largely it’s a matter of time and distance. The farther away in both your thermometer is from a spurious or transient heat source, the less effect it has on the reading. Which is why the buoys at a reasonable depth are really quite good about things.

But for implicating the assumed fractional blame of that on humanity requires that you first have a fully useful (predictive value in forecasting) model of the climate. If, from that, you have a straight up correlation of CO2 to Temperature, then you can take the known natural carbon sources/sinks by isotope ratio, the human output of CO2 by isotope ratio of the carbon in the fuels we use, and then compare that to the isotope ratio of carbon in the atmosphere.

Difficulty: We do not have a model of climate that produces any useful forecasts. The IPCC models have been shown to be bested, on every metric of interest by a coin flip. And as Stokes claims, Anthropogenic Global Warming implicates that the temperature can both increase and decrease in the face of increased atmospheric CO2. Or simply, there are no predictive models, and the scientific theory posits no correlation between CO2 and temperature.

“Global sea level is currently rising as a result of both ocean thermal expansion and glacier melt, with each accounting for about half of the observed sea level rise, and each caused by recent increases in global mean temperature. For the period 1961-2003, the observed sea level rise due to thermal expansion was 0.42 millimeters per year and 0.69 millimeters per year due to total glacier melt (small glaciers, ice caps, ice sheets) (IPCC 2007). Between 1993 and 2003, the contribution to sea level rise increased for both sources to 1.60 millimeters per year and 1.19 millimeters per year respectively (IPCC 2007).”

The contribution from groundwater sources is significant. I’m making this point related to how much it is causing ocean levels to rise. However, our impossible to sustain rate of pulling a dwindling supply of underground water out for human activities………..in essence, wasting this abundant natural resource is the legitimate catastrophe of the future.

Ironically, increasing CO2 levels benefits crops/plants most in their root mass. More developed roots can access more nutrients, including water. As a result, plants grown with higher CO2 levels need less irrigation and conserve this precious natural resource.

It is an absolute certainty that our future world will suffer grave consequences because of this generations wasting of massive underground water supplies like the Ogallala Aquifer in the Plains. When this water supply is gone………….it’s gone.

The impact of Ozone depletion caused by volcanoes has been greatly under-appreciated.

I’ve been waiting for the lower stratosphere to start warming up, signalling that the Ozone has started to rebuilt. So far, it hasn’t really shown up but the lower stratosphere has been stable or increasing slightly for 18.5 years now.

It may take up to 25 years for the Ozone to rebuild after the large stratospheric eruptions. Fortunately, they only happen 3 or 4 times a Century.

Does the lower Ozone also affect the surface and lower troposphere. Well, it does let more UV solar radiation in so the answer must be Yes. I note Troy Masters has a new paper out which ponders if volcanoes produce long-term warming. Ozone depletion would be the mechanism for that.

“Just The Facts”. I am very pleased with you. You have, as is usual, done a very good job. – A job that I cannot but just applaud.

And not fault – at all

However I can no longer understand why we keep on giving these “Climate Cowboys” more and more rope. – They hung themselves – at least once – a long, – very long – time ago.

Let us, since you call yourself “Just The Facts” look at – just the facts – i.e. “IR radiation is “all around us. We use it here, there and everywhere in things like sensors for all manner of things: – opening doors – switching lights on and off – remote controlled burglar alarms, you name it. It is there; “IR radiation is real”. – But, – Yes, – but where is the “temperature Interchange???”

Scientists who believe that say 10º C can become 11º C – once it has been carried “to and fro” on the back of CO2 wants to have their heads examined. Well that is only my opinion and I know many “Lukewarmers will disagree” – Well, there is no shortage of IR radiation. There is however a shortage of proof for “IR Heat-exchange”

“Global warming is the unusually rapid increase in Earth’s average surface temperature over the past century primarily due to the greenhouse gases released by people burning fossil fuels.” –NASA’s Earth Observatory

Unusually relative to what? And what about temperatures that were just as high as in the past? Those can’t be attributed to people burning fossil fuels. Primarily? In a pig’s eye. Global heat balance can’t be measured with surface temperatures, which ignore humidity and phase change data. Many instances of high atmospheric temperature constitute net heat-shedding mechanisms. Trying to measure global heating with atmospheric temperatures is like trying to estimate the population of a city by counting the number of cars driving out of it on a freeway. NASA’s ignorance is only exceeded by its hubris and stupidity.

Crudely, GHG’s are like a blanket on the Earth. And the stratosphere is above the blanket. If you thicken the blanket on your bed, you get warmer, but the cat on top gets colder.
>>>>>>>>>
Nick, you might want to look at the basic heat transfer equation.

Nick Stokes: “No. GHG’s affect different levels of the atmosphere differently. I’m talking about the stratosphere.”

My apologies, I misunderstood. So you’re not saying that AGW heats and cools or neither heats and cools, but that it A) heats in once place and B) heats in another. So your argument is that given A and B, and given that A is false, the hypothesis is true because… B is. Which admittedly works if the AGW hypothesis is that it will heat there or cool there.

But then I’ve never heard that. So is it falsified? Or is the actual hypothesis that they don’t know if it will heat or cool, but that if it does either or both the heating and cooling will happen in different places?

Contrary to assertions made by articles from which you quote it is not global surface air temperatures that have been constant during the pause. Rather it is temperatures along a linear trend line that have been constant. That temperatures along a linear trend line have not changed does not imply that global warming has paused for the “global warming” is the increase in the global surface air temperature.

Terry Oldberg says:
November 15, 2013 at 6:14 pm
That temperatures along a linear trend line have not changed does not imply that global warming has paused for the “global warming” is the increase in the global surface air temperature.
>>>>>>>>>>>>>>>

Look at it this way, Terry, moving those goalposts is hard work, but it gets you your exercise….

The most important graph is the South Polar Troposphere. The south pole has a unique climate with very little water vapor. Hence, this is where the impact of CO2 should be the most significant. It also has the strong circumpolar winds to limit the influence from the rest of the planet. This should be an area showing the most warming. Instead, we see – .011º/decade.

If CO2 has no influence over Antarctica it won’t have any influence elsewhere.

dbstealey says: November 15, 2013 at 5:51 pm
“If Nick Stokes or anyone else has a problem with what the graphs are saying,”

I don’t have a problem with what the graphs are saying. I just note that, while they are included in a general narrative about the pause (Santer etc), it has always been standard AGW theory that adding GHGs warms the surface and cools the stratosphere, as observed.

Jquip says he’s never heard that. Well, I quoted AR3, and Jeff Masters. Here is a plot from the classic paper of Manabe and Weatherald, 1967, clearly showing what is expected. They didn’t know about ozone depletion then. h/t this discussion in Science of Doom.

iNick Stokes says:
November 15, 2013 at 6:47 pm
it has always been standard AGW theory that adding GHGs warms the surface and cools the stratosphere, as observed.
>>>>>>>>>>
And, as observed, standard AGW theory is WRONG. Nick, why do you think they try to come up with the new label “climate change”, duh?

Well, I quoted AR3, and Jeff Masters.
>>>>>>>>>>>>
Not very good sources for the TRUTH, if that is what you are seeking.

Nick is correct guys. GHG’s in isolation from all other effects result in the Mean Radiating Level to increase in altitude. Anything below the MRL becomes warmer and everything above it becomes cooler. The debate is about the feedback effects of this occurring, both their sign and magnitude.

The debate should also be about SB Law dictating that the largest of these effects will be at low temps (night time, winter, high latitude and high altitude) and the effects minimized at high temps (day time, summer, low latitude and low altitude) but apparently that’s just too complicated a discussion for the bulk of people on both sides of the debate to follow, so I just get ignored when I bring it up.

Opportunities for hilarity are presented by both sides in the argument over whether continuing emissions of CO2 are or are not seriously harmful. My level of hilarity is diminished by the fact that this state of affairs is starting to cost me a lot of money!

So you’re saying that Santer’s statements about the lower troposphere were actually about the stratosphere? So now your claim about the official hypothesis of AGW is that they don’t know if it will heat or cool, but if that if it does either or both it won’t be in the same place, but that none of those places will be the place the theory claimed it would be.

Since this is all about falsification, at which point do you suggest that I discard the null hypothesis that you possess both a minimum knowledge of the topic and a minimum of honesty?

Contrary to assertions made by articles from which you quote it is not global surface air temperatures that have been constant during the pause. Rather it is temperatures along a linear trend line that have been constant.

Which articles and assertions are you referring to? I don’t think that anyone thinks that seasonality has been eliminated and Earth’s temperature is now constant due to the Pause. Do you?

That temperatures along a linear trend line have not changed does not imply that global warming has paused for the “global warming” is the increase in the global surface air temperature.

Can you please provide links to graphs and/or data that shows the “increase in the global surface air temperature” that you reference?

Jquip: please cut it out. Nick Stokes (and others) has explained that AGW theory predicts that the troposphere gets warmer and the stratosphere gets cooler, and from 1975 to 2000 this theory seemed to be going swimmingly. But even during that period sane people knew that there was more to climate than just CO2, and that solar influences (about which there is a lot of argument) and ocean “oscillations” could have played a part.

Just the Facts: Your article is interesting but a bit too long. It is extremely unfortunate that you portrayed the stratospheric temperatures at all since that has confused some readers such as Jquip.

I find the “20 Year Northern Hemisphere Snow Cover with 1995 – 2009 Climatology from NCEP/NCAR” interesting, as in the anomaly the “middle” years seem to be simply “noisy”, while towards the “fringe” (1995 or 2009) there seems to be a correlated yearly signal.

One possible explanation is that the amplitude stays (more or less) the same, while the “phase” (of signal vs. average) shifts – as in earlier seasons, or later seasons.

Does this happen in other 25 years intervals?

Or in other datasets (temperature, precipitation, and so on)?

If so, then there are subtleties of the weather that are not well captured by these types of diagrams. And that these diagrams show a bigger anomaly than is actually present in reality.

“GHG’s in isolation from all other effects result in the Mean Radiating Level to increase in altitude. Anything below the MRL becomes warmer and everything above it becomes cooler.”
>>>>>>>>>>>>>>
This sounds like something Mosher would say, except he likes to call it “ERL”!
You should offer a disclaimer that this is your “belief”, not science. Hint: If you don’t know where the “MRL” is, then it probably doesn’t exist. (But you can believe whatever you want to.)

Well, as I said, ozone depletion was the main factor. But GHG’s were expected to have a cooling effect too. And it cooled.
=======================================================================
Ozone depletion by CFC’s? According to the ozone hole plot, the area is ~0 after 50 years of CFC use, then dramatically increases, then dramatically levels off after the Montreal Treaty. Are we to assume that the ozone hole was zero all times before 1979 and that there are no other ozone depleting chemical sources natural or man made? When I was going through all the expensive ozone depleting chemical shenanigans it seemed that the kinetics were a tad shaky and that we lacked long term data on the ozone hole and upper atmospheric ozone. I believe we still lack those trends to make any valid conclusions on ozone depletion.

So, how long until “the pause” is longer than the warming that started the Big Scary Story in the first place? We must be getting quite close to that point – eyeballing the temp graphs suggests that the scary up-tick started between about 1975 and 1980, which would mean that, within the next 2 to 8 years, the pause will have outlasted the increase.

Seems to me that’s a message that the general public could understand intuitively when it happens.

Some people say that the ozone hole has always been there, exacerbated slightly by cfcs.

There’s an assumption that people make that the famous Ozone holes are man made. While some pollutants can in fact destroy Ozone, the holes themselves are in fact natural.

Ozone exists as a layer of gas in the earth’s atmosphere. The layer right underneath it is Oxygen. Both are made of the same atoms (O) but Oxygen is two of them stuck together (O2) and Ozone is a threesome (O3)……

So is the Ozone hole a complete hoax? Pollutants like CFC’s could make the holes larger in theory, but the fact is that the holes are natural in the first place, and they fluctuate daily as the earth spins, seasonally as the earth’s inclination to the sun changes, annually as the earth’s orbit takes it closer and farther away from the sun, and from fluctuations in the sun’s output of UV in the first place.http://knowledgedrift.wordpress.com/2010/05/22/ozone-the-hole-that-always-was/

See – owe to Rich: “Nick Stokes (and others) has explained that AGW theory predicts that the troposphere gets warmer and the stratosphere gets cooler, and from 1975 to 2000 this theory seemed to be going swimmingly.”

So you’re saying that Nick Stokes explained the theory that he didn’t explain and claims that it no longer works after claiming there were no problems with it? You seem about as well informed and coherent as Stokes does.

Here’s a hint for you though: The temperature/radiation profiles in the troposphere and stratosphere are related to the density profile of the atmosphere, temperature, as the gas constituents. For every imaginable gas you can consider you will get the same results tinkering with any of them. This extraordinarily obvious mechanism has no relation to AGW whatsoever. It is wholly and completely independent of the AGW theory.

But given the magic Devil Gas of interest in these discussions, and our ballpark knowledge of its concentrations, then you can solve the rest of the equations if you know just and only temperature. The options here are a) Send up balloons and receive UFO sighting reports, b) go Roger Ramjet with spacecraft, and c) Find some manner to correlate the Devil Gas and temperature.

Note that c) is lovely for a number of reasons, but that it doesn’t require that the Devil Gas causes heat, the other way around, or anything else. So long as they are not spuriously correlated,, and it tracks well, then we can model it with a single parameter. The AGW side of things is nothing more than the claim: Devil Gas cause Hella Heat. eg. Screw raw correlation, CO2 causes Temperature.

And for all his yapping out ‘true’ predictions that have no connection to AGW, this is the part that Stokes and the dissembling crowd that dreams of fairy dust and starving kulaks don’t want to talk about: The only reason that Santer’s 10 and 17 years claims are interesting is *not* because of completely obvious things about gas pressures that have nothing to do with AGW. It’s because Santer was claiming, at that time, that AGW had not properly correlated CO2 and temperature. For Santer to assign a fraction of human blame to it, he needs that correlation — regardless of causation — to pull it off.

But that’s just the thing, if the AGW hypothesis has *already and properly rejected the null hypothesis* then Santer’s statement is never: “I need 17 years” it is “The science already shows.” And that’s why you get the Dog and Pony magic show from the hucksters and patent medicine peddlers such as Stokes. Because to acknowledge this at all is to acknowledge that Santer *has already claimed by his 17 years* that the AGW thesis or correlation has yet to be tested — just one time — or that they have — like so many recent science publications — spuriously rejected the null hypothesis.

And that’s why you get a load of fast hand-waving from the sophists like Stokes. Who refuse to make any claims, or even state plainly what the AGW hypothesis is. And it is why he link drops idiots like Masters to try to avoid explaining what the issue is. Because if they do any of these things: They will be exposed as mendacious idiots.

geran;
This sounds like something Mosher would say, except he likes to call it “ERL”!
You should offer a disclaimer that this is your “belief”, not science.
>>>>>>>>>>>>>>>

ERL and MRL are the same thing, and you can find my “belief” in any thermodynamics text that addresses this particular subject. You can find the equations that describe my “belief” and you can find the lab experiments that confirm my “belief”, you can even do them if you want. Then you’ll be educated enough to know what you are talking about instead of shooting your mouth off. I’m no warmist, I’m a skeptic, but there are portions of GHG theory that are very well accepted by physicists on both sides of the debate and this is one of them.

“GHG’s in isolation from all other effects result in the Mean Radiating Level to increase in altitude. Anything below the MRL becomes warmer and everything above it becomes cooler.”
>>>>>>>>>>>>>>
This sounds like something Mosher would say, except he likes to call it “ERL”!
You should offer a disclaimer that this is your “belief”, not science. Hint: If you don’t know where the “MRL” is, then it probably doesn’t exist. (But you can believe whatever you want to.)
——————
I am having a little difficulty understanding the significance of the MRL.

Genghis;
How does a changing lapse rate affect the MRL?
>>>>>>>>>>>>>>>>>>

I suggest studying Stefan-Boltzmann Law and Planck. When you understand those to the point where you can apply them, read through Willis Eschenbach’s “Steel Greenhouse” articles on this site. If you want another approach to the subject that starts at a more basic level, I recommend the series by Ira Glickstein, the links to which I keep handy:

The answer to your question is that a change in the MRL affects lapse rate rather than the other way around, but that’s a gross over simplification. It is a very complex dynamic once you get into a lapse rate discussion. Which is why I said that in the absence of all other effects everything below the MRL gets warmer and everything above gets cooler. Once you get past those effects in isolation, complexity happens uber fast.

Some people say that the ozone hole has always been there, exacerbated slightly by cfcs.

I have never seen any observational evidence that the “ozone hole has been exacerbated slightly by cfcs” but there is extensive evidence that the “ozone hole has always been there” and is likely a result of the dynamical effect of the stratospheric polar vortex i.e.:

“Air from very high altitudes descends vertically through the center of the vortex, moving air to lower altitudes over several months.” NASA

“The walls of the polar vortex act as the boundaries for the extraordinary changes in chemical concentrations. Now the polar vortex can be considered a sealed chemical reactor bowl, containing a water vapor hole, a nitrogen oxide hole and an ozone hole, all occurring simultaneously (Labitzke and Kunze 2005)” Stratosphere troposphere interactions: an introduction

“caused when an area of low pressure sits at the rotation pole of a planet. This causes air to spiral down from higher in the atmosphere, like water going down a drain.” Universe Today

“A polar vortex is a persistent, large-scale cyclone located near one or both of a planet’s geographical poles.” “The vortex is most powerful in the hemisphere’s winter, when the temperature gradient is steepest, and diminishes or can disappear in the summer. The Antarctic polar vortex is more pronounced and persistent than the Arctic one; this is because the distribution of land masses at high latitudes in the northern hemisphere gives rise to Rossby waves which contribute to the breakdown of the vortex, whereas in the southern hemisphere the vortex remains less disturbed. The breakdown of the polar vortex is an extreme event known as a Sudden stratospheric warming, here the vortex completely breaks down and an associated warming of 30-50 degrees Celsius over a few days can occur. The Arctic vortex is elongated in shape, with two centres, one roughly over Baffin Island in Canada and the other over northeast Siberia. In rare events, the vortex can push further south as a result of axis interruption, see January 1985 Arctic outbreak. Wikipedia

“The ozone hole is in the center of a spiraling mass of air over the Antarctic that is called the polar vortex. The vortex is not stationary and sometimes moves as far north as the southern half of South America, taking the ozone hole with it.” NASA

Earth’s climate system is ridiculously complex, as a multitude of variables and measurement capabilities continue to develop, hence this article is likely to only grow longer. There is actually a significant audience for these large data compilations, hence why I generate them. However, I understand your point and am considering generating a separate more succinct version of this article to assure that is accessible to a broad audience.

It is extremely unfortunate that you portrayed the stratospheric temperatures at all since that has confused some readers such as Jquip.

I don’t understand your logic here. I think it is fortunate that I portrayed stratospheric temperatures because this offered WUWT a fuller picture on “Earth’s Temperature” and elicited a healthy conversation and debate around the subject.

davidmhoffer says:
November 16, 2013 at 7:23 am
“I’m no warmist, I’m a skeptic, but there are portions of GHG theory that are very well accepted by physicists on both sides of the debate and this is one of them.”
>>>>>>>>>>>>>>

Yeah David, but you are not an EXTREME skeptic. If you continue to study the science you will get there because I often read your comments, and you are not a dummy. You just need to understand, as do many, that we can no longer trust public entities, mainly government and academia. They are lying to us. Their science is heavily slanted, if not entirely false. We have entered the new “Dark Ages”.

All the different methods they use to keep the fear of CO2 alive continue to fail. Like I hinted before, ask them the exact elevation of the “ERL” or “MRL” right now. And, within a year or two they will have a new fancy explanation for why the CO2 is heating up the planet, but there is no evidence of it. Like one commenter here said a month or two ago, it’s like playing “Whack-a-mole”.

geran;
I’m not an EXTREME skeptic? LOL. I frequently describe myself as a “raging skeptic”.

In any event, Stefan, Boltzmann, Planck, Einstein and many others are on my side on this point. I’m a raging skeptic because I HAVE studied the science. It is of little value in this debate to be right for the wrong reasons, which is where you are at right now.

To try and simplify it for you, the Stefan-Boltzmann Law is:

P=5.67*10^-8*T^4

With P in watts/m2 and T in degrees Kelvin. If you know the amount of energy flux an object is exposed to in w/m2, and its albedo, you can calculate its equilibrium temperature. We know those numbers for earth and the equilibrium temperature is 255K. The surface temperature however, is 288K, 33 degrees higher. How can this be true and Stefan-Boltzmann Law also be true?

Stefan-Boltzmann Law describes the temperature of a surface. The earth as seen from space has a surface surrounded by a fuzzy sorta thing called an atmosphere. For the earth to be in equilibrium, energy must be radiated from earth to space in the amount calculated by SB Law. BUT, it doesn’t get radiated from the surface. Some of it gets radiated from the surface, some from the lowest reached of the atmosphere, some from the middle, some from the top.

If you could view the earth from space with an IR thermometer, you would read a temperature that exactly equals the SB Law calculation. But your IR thermometer only knows the total number of photons per second and their energy levels that it is seeing. It doesn’t know if they came from the surface, lower, middle, or upper atmosphere. It only knows the average of what it sees and calculates temperature from that.

If you were to measure the temperature of the atmospheric column from surface to TOA at thousands of altitudes, and average it, you would get the exact same number. Now double CO2 and wait for equilibrium to be once more established.. From space you would STILL see the exact same number. If you measured the temperature at thousands of points from surface to TOA you would ALSO get the exact same number.

BUT, the lower altitude numbers would be higher and the high altitude numbers would be lower, and the average would be the same.

One reliable aspect is that temperature increase is reported where people ain’t. The classical example is the Antarctic peninsula where all manned bases are on the west side because the east side is too cold — so of course they report that the east side has warmed three times as much as the west — but not enough to move any manned base there, of course. Easy to report phony temperature increases where there are no witnesses.

I calculated that number for myself from known physics over 20 years ago well before I ever heard of this debate. No point explaining further since you have declared your refusal to even read the explanation. You are exactly the same as the raging warmists who equally don’t have a clue what they are talking about, you’ve made up your mind and refuse to even consider reading factual information that disagrees with your point of view.

The SB equation requires an ideal absorber so that it can be properly applied. Assume TSI of 1365 W/sq.m, and albedo of .3, then 955.5 is the number we use in the SB equation. So, solving for T, we get 360K.

The “politically correct” [WRONG] pseudo-science wants us to divide the 955.5 by 4, but there is no “divide by 4″ in the SB equation.

Wow geran. So according to you the correct temperature of earth is just below the boiling point of water? Did you stop to think through the stupidity of making such a claim?

SB Law is predicated on the average TSI. Since the sun shines only on half the earth at one time, you must first divide by 2. Then you must account for the fact that the earth is round and so even on the side with sunshine, while the TSI at the equator at noon might be 1365, it tapers off to zero at the poles and at the edges of the lit area. If you do the geometry, you’ll find that dividing by 2 again gives you a fair approximation for that.

But feel free to continue demonstrating your complete ignorance of the subject. I’m done with you.

One of the problems with ERL/MRL conjecture is that it is based on energy radiated from the surface in isolation. That is, it ignores all the energy in the atmosphere. By itself it follows from basic physics, but it is not by itself and the “other stuff” is quite important. Like most of global warming science it is nothing but a half truth.

CO2 and other GHGs increase the flux of energy from the atmosphere to space. This process in isolation would lead to a lowering of the ERL/MRL. As far as I’ve been able to discover, no one has looked at the affects of both of these processes in combination in any detail. However, given the stability of our temperature across a billion years despite significantly different CO2 levels. I have a distinct feeling they come close to cancelling each other out.

davidmhoffer: “If you do the geometry, you’ll find that dividing by 2 again gives you a fair approximation for that.”

Uh, that only works for a flat disc and – which does *not* taper off – and is under the idea of converting surface area to surface area. If you take the flux incident on the sphere given the angle of the sphere, it is decidedly different for the average flux. And as T is non-linear with respect to flux you get a different answer still if you take T before you take the average flux.

Angles on a pin though, really. At least, so long as no one gives too much credibility to absolute temperatures derived from impossible geometry constructed out of non-rotating unobtanium.

davidmhoffer says:
November 16, 2013 at 11:20 am
“Wow geran. So according to you the correct temperature of earth is just below the boiling point of water?”
>>>>>>>
See, I said earlier you were not a dummy. To be accurate, 360K = 87ºC, 189ºF (The implication is, of course, that the Earth has cooling mechanisms that can easily handle the excess solar energy.)

“Did you stop to think through the stupidity of making such a claim?”
>>>>>>
It’s exactly how the math turned out. The stupidity is in trying to “spin” it around, as Warmists attempt.

“SB Law is predicated on the average TSI.”
>>>>>>>>
NOPE, SB Law is a mathematical relationship between E/M energy and temperature. The equation just calculates the corresponding temperature for any level of TSI.

“Since the sun shines only on half the earth at one time, you must first divide by 2.”
>>>>>>>>>
NOPE, you have just invalidated the results. The SB temp must coincide with the actual insolence, not some estimated average value.

“Then you must account for the fact that the earth is round and so even on the side with sunshine, while the TSI at the equator at noon might be 1365, it tapers off to zero at the poles and at the edges of the lit area. If you do the geometry, you’ll find that dividing by 2 again gives you a fair approximation for that.”
>>>>>>>>>
NOPE, the SB equation does not calculate well with “fair approximations”. You MUST use the equation based on the conditions of its derivation. Making up approximations is the pseudo-science you need to run away from.

“But feel free to continue demonstrating your complete ignorance of the subject. I’m done with you.”
>>>>>>>>
“Demonstrating complete ignorance” is taking a precise equation and dividing the input by 4. You cannot “divide by 4″, make up excuses, and expect the answer to mean anything. But, you are free to do that. Heck, “divide by 5″ and call it “fried chicken” if you want. Or, “divide by 6″ and call it a “1957 Chevy”. But, it is all pseudo!

(I suspect that you really want to learn, but are just confused by all the nonsense out there. Feel free to come back whenever you desire.)

I’d say our temperatures have been stable, ie fluctuating within about a ten degrees C range (~12 to 22), since over 540 million years ago (when the sun was around 5% less powerful), but not a for a billion years, which would include Snowball Earth intervals.

Really not terribly sure what your point is. Yes that’s the correct ratio of surface area from a disk to a hemisphere. Or 1/4 to a whole sphere, which is the ‘approved’ manner of calculating the black body temperature of a planetary body. It’s also quite wrong, as the flux is in m^2 and is modulated by the angle of incidence on the surface of a sphere, not the angle of incidence on a circular wall called Earth.

Savvy up with Euclid and go sort out the average height of a hemisphere and why that makes any difference.

“I’m not an EXTREME skeptic? LOL. I frequently describe myself as a “raging skeptic”.
In any event, Stefan, Boltzmann, Planck, Einstein and many others are on my side on this point. I’m a raging skeptic because I HAVE studied the science. It is of little value in this debate to be right for the wrong reasons, which is where you are at right now. —– — – — – -.We know those numbers for earth and the equilibrium temperature is 255K. The surface temperature however, is 288K, 33 degrees higher. How can this be true and Stefan-Boltzmann Law also be true?

= = = = = = = = = = =

I do suspect that you are using one of the editions of “Kiehl & Trenberth’s Earth’s Annual Mean Energy Budget” plans as a basis for your calculations, which divides the so called “Solar Constant” by 4 (don’t worry – I do know the calculus or formulas for areas of discs & spheres) which has the effect of portraying a situation that happens nowhere in this “Solar – System.” As long as you carry on using ¼ of the ‘Solar Irradiation’ in your calculations you will carry on being wrong.

It is easy really, because if you ““Know” the “equilibrium temperature”” is 255K but that the surface temperature is 288K, 33 degrees higher, then it is more likely your calculations are wrong – and that the “measured” surface temperature is “near enough” correct. – So – Ditch the K&T plan – and wait, patiently until all the necessary temperature data are in – – – – – – -.

You see when you talk about temperature (T) of the surface. You cannot ignore facts. One of these facts is that the Earth stores heat (T) in the ground. Try for example to find out where the T from the planet’s core meets the solar induced T percolating downwards from the top of the surface. – Too complicated? – not enough data? – too many problems? If so then that’s correct, but if you want the right answers – there are no short-cuts.
Remember also that Trenberth, who is the one best known by us here on WUWT, is an EXTREME CAGW enthusiast. –

I suggest that you take a look at the science as it was before Arrhenius and his misunderstood back radiation nonsense, i.e. write “Fourier 1824” into your search engine and see what “The father of the GHE” had to say about it. – And while you are at it, look up “John Tyndall” in the same manner. –

There is a GHE, yes sure there is, but it has to do with the fact that “The GHGs” that are in contact with the surface “block” the path of “Energy- radiation” away from the surface. Nothing to do with “Back-radiation” – at all. Once the energy has left the surface as ‘IR radiation’, there is no way back into the surface for it. IR radiation cannot penetrate solids – not even transparent solids like glass – nor can it penetrate fluids or liquids like water. – Just think about it – We just have not, as yet, got the “necessary correct numbers to work it all out”

Jquip;
Really not terribly sure what your point is. Yes that’s the correct ratio of surface area from a disk to a hemisphere.
>>>>>>>>>>>>>>>>>>

From the sun looking at the earth, the earth presents as a disk. The total joules/s being radiated into the earth is the area of the disk times the TSI. The area of the hemisphere being twice the area of the disk, the w/m2 averaged over the area is 1/2 the TSI. Given that only 1/2 the earth is being radiated at any given time, the average for the earth is 1/4 the TSI.

O H Dahlsveen;
I do suspect that you are using one of the editions of “Kiehl & Trenberth’s
>>>>>>>>>>>>>>>>>.

davidmhoffer: “From the sun looking at the earth, the earth presents as a disk. The total joules/s being radiated into the earth is the area of the disk times the TSI.”

In raw Joules, sure. But we’ve been talking about this “With P in watts/m2 and T in degrees Kelvin.” (Your quote) the whole time. Now project a unit meter over the surface of a sphere. If you’re absolutely certain there’s no difference then TSI/2 will be equal to TSI * average height of a unit hemisphere. But that would be 2TSI/3. Which is.. yeh, not the same.

So I’ll leave it to beaver. Since no more than one of those can be correct: You go figure out how a unit square projects on an incline or conic.

The Arctic vortex is elongated in shape, with two centres, one roughly over Baffin Island in Canada and the other over northeast Siberia.
=================
strange that the vortex would align with the dual magnetic poles in the N hemisphere.

davidmhoffer: “I was right the first time. You failed grade 10 geometry.”

And you have sex with underage girls. Every assertion is awesome without reasoning, yes? Or you could take that path Stokes failed, the one of the knowledgable and honest man and show why any of the following are false:
1) The SB law doesn’t use watts/m^2 as you stated.
2) That a unit square projected on a plane 60 degrees off the perpendicular doesn’t cover two unit squares.
3) That a sphere is not a set of infinitely small planes at different inclinations.
4) That the average height of a hemisphere is not equal to a plane inclined at 60 degrees

And you have sex with underage girls.
>>>>>
Jquip, I have taken numerous insults from David today, only trying to help him understand. He has insulted you also. But, do not get down in the mud with him. If he is a phony, he will try to bring you down to the bottom with him. If he realizes he has been misled, he will be appreciative of our efforts.

The surface area of a Sphere is 4πR^2 which converts to 1/4 for a perpendicular area. So if the S-B law is applied with emissivity matching absorptivity of 1366 W/m^2 the answer is 279K (6˚C) or exactly the average temperature of the oceans.

And yes Davidmhoffer I am familiar with S-B, Planck, Kirchoffs (I am an EE), etc, but mostly I am a sailplane pilot and sailor. I am also convinced that evaporation from the ocean controls the earths surface temperature.

The WUWT post “GHCN’s Dodgy Adjustments in Iceland” is worth studying in this regard.http://wattsupwiththat.com/2012/10/15/ghcns-dodgy-adjustments-in-iceland/
It really ought to be named: GHCN’s Adjustments shown to be Dodgy BY Iceland Iceland has several, at least six, long record, well located professionally run temperature stations. Yet GHCN sees fit to adjust these readings.

The “Pairwise Algorithm” is claimed to isolate non-climatic changes by comparison with other stations. But in Iceland this clearly has not happened. Every single station exhibits the same trend and at every one the algorithm has adjusted it out. There are no stations [in Iceland] that the algorithm could possibly have used to have come to the conclusions that it did.

It is impossible to come to any other conclusion than that the software is hopelessly flawed.

As I put it in comments then:Iceland is THE control. It is the laboratory where the algorithm must work in isolation. If the Algorithm breaks on Iceland, the algorithm is broken. If the algorithm gives untrustworthy results because of human error, the entire process is untrustworthy.

JustTheFacts: OK, I concede it to you, this thread is actually valuable for education. First off (well, second chronologically) davidmhoffer has to explain to others that radiative physics has to allow for a 1/4 factor because the area of a sphere is 4*pi*r^2 whereas the area of a disk is 1*pi*r^2. It is disappointing when readers don’t allow for physicists to get even the basic things right. After all, without an atmosphere and an ocean the physics would be relatively straightforward.

And second off, Jquip, whom I am beginning to admire for eloquence if not understanding, needs to understand that greenhouse gases can warm the troposphere whilst cooling the stratosphere. Actually, I can understand his/her quibbling on this point, as it does seem counter-intuitive. But if Nick Stokes, who I believe understands more physics than I do, has references to explanations which I understood on at least one occasion then that is good enough for me. Ultimately of course, this is what separates luke-warm sceptics from dragon slayers: the former believe there is a basic greenhouse effect but hotly dispute the magnitude and even sign of feedbacks, and the latter dispute the basic effect.

Jquip;
Following is an experiment I actually performed some 30 years ago to explain to a very distraught first year engineering student why she had just failed her first first term physics exam:

Take a round flat piece of cork. Insert into it any number of tooth picks, I used 10. Insert them such that they are evenly distributed, and vertical when the flat side of the cork is horizontal. Now, take a rubber ball of the same diameter as the cork. Center it over the cork, and press down. The tooth picks in the center of the cork will contact the ball first, but if the ball is sufficiently soft, you will be able to press the ball down far enough, without deforming it, such that each tooth pick makes a tiny dent in the ball. Now remove the ball and observe that

a) the dents from the tooth picks are distributed closer together at the center of the ball than at the edges
b) the number of dents in the ball matches the number of tooth picks exactly
c) the number of dents per unit area of the ball as a whole is precisely 4 times the number of tooth picks per unit area of the flat side of the cork.

I should just add that I have ever so slight second thoughts about whether Geran and Jquip between them are arguing over whether some averaging process is illegal, or more correctly put, inaccurate. But then only mathematics can answer, and they don’t specify the integral which they believe to be correct. But probably they aren’t mathematicians – I’m not sure.

So if the Earth had no atmosphere and ocean and seasons and one treated each infinitesimal part of it as having separate temperature and radiation, what would be the mean temperature of the Earth? Well, I _am_ a mathematician, but it’s way too late at night here in England.

See – owe to Rich says:
November 16, 2013 at 3:37 pm
I should just add that I have ever so slight second thoughts about whether Geran and Jquip between them are arguing over whether some averaging process is illegal, or more correctly put, inaccurate. But then only mathematics can answer, and they don’t specify the integral which they believe to be correct. But probably they aren’t mathematicians – I’m not sure.

So if the Earth had no atmosphere and ocean and seasons and one treated each infinitesimal part of it as having separate temperature and radiation, what would be the mean temperature of the Earth? Well, I _am_ a mathematician, but it’s way too late at night here in England.

Rich.

>>>>
Ever so well stated Rich. (Now could you translate that into English for us?)

It’s not terribly germane. If the disc model is right, then you can start with the geometrically accurate model and reduce it to the disc and retrieve the same value. The numbers and arguments are all given, so if you’ve got a proof produce it. Or, more to the point, as you’ve been given the whole thing simply show where it is invalid. Otherwise it’s just yapyapyap.

It’s not terribly germane. If the disc model is right, then you can start with the geometrically accurate model and reduce it to the disc and retrieve the same value. The numbers and arguments are all given, so if you’ve got a proof produce it.
>>>>>>>>>>>>>>>>>>>

I just did!

Oddly, when I discuss physics with PhD physicists, I’m apparently a pretty bright guy. When I discuss physics with you, I suddenly become a dolt. Not wanting to be a dolt, I surrender the field.

No, you did not. Not unless you want to claim that the sun is inside the Earth, or surrounding it as a shell, and that it projects perpendicularly at all points on the surface of the Earth; save one hemisphere. This. Is. Obviously Wrong.

In fact, the sun sits off to one side by about 1AU. A distance large enough that we can consider that the radiation it project at Earth can be considered parallel to the plane of the ecliptic. Now, what is the flux incident on each square meter *on the Earth’s surface* as represented as its inclination from a plane perpendicular to the radiation projected *at it*?

Let me take it slowly then: Draw a line between the center of the Sun and the center of the Earth (Point A) and let the intersection of that line with the surface of the Earth be Point B. Then for any other point on the sunlit surface of Earth (Point C) we have the angle described by ABC. Let ABC be 60 degrees. Then if one unit square of sunlight is incident on a plane at that angle, it will fall on? 2 unit squares. Such that if the flux/m^2 is F then each unit square has F/2 flux/m^2 incident upon it. This is straight up obvious as stating F * Cosine(ABC). You may repeat this freely for any arbitrary point on the sunlight hemisphere.

For finding the average flux/m^2 incident on the surface of that sphere you might recognize that this is *exactly the problem* of the average height of a hemisphere with a unit radius. Go. Now. Google up a picture of the problem and the integrals to use; or just the answer. That is, the average height of the hemisphere of unit radius is the average value of the cosine of ABC for every possible C on that surface. That is your geometrically accurate model. And for our value F it gives 2F/3 as the average incident flux/m^2.

Jquip says:
November 16, 2013 at 4:54 pm
Now, what is the flux incident on each square meter *on the Earth’s surface* as represented as its inclination from a plane perpendicular to the radiation projected *at it*?
>>>>>>>>>>>

Your method of computing the flux incident to each square surface meter of a hemisphere will exactly equal the total flux incident to the area of a circle.

Where your method is superior is in actually computing the temperature and black body radiation for a particular square meter.

Genghis: “Where your method is superior is in actually computing the temperature and black body radiation for a particular square meter.”

For a single square meter, sure. For speaking about the average flux per square meter across the surface, sure. (eg. Radiation balance models/graphs) But you get different results from taking T from the average flux and taking the average T from flux per locus. I did it once and long enough ago that I don’t remember the particulars off hand save that both were significantly different from the common TSI/4. But I couldn’t tell you more than that the math was nasty enough that I didn’t chase it further.

For a single square meter, sure. For speaking about the average flux per square meter across the surface, sure. (eg. Radiation balance models/graphs) But you get different results from taking T from the average flux and taking the average T from flux per locus. I did it once and long enough ago that I don’t remember the particulars off hand save that both were significantly different from the common TSI/4. But I couldn’t tell you more than that the math was nasty enough that I didn’t chase it further.
>>>>>>>>>>>>>>>>

What is wrong with my simple calculation that produces an equilibrium black body radiation of 279K which correlates almost exactly with the average temperature of the ocean? I just divided 1366 by 4 and applied the S-B with absorption equalling emission (Kirchoffs law).

Genghis says:
November 16, 2013 at 7:05 pm
What is wrong with my simple calculation that produces an equilibrium black body radiation of 279K which correlates almost exactly with the average temperature of the ocean? I just divided 1366 by 4 and applied the S-B with absorption equalling emission (Kirchoffs law).
>>>>>

The 1366 must be adjusted by albedo (0.3) to 956 because that is the actual flux reaching Earth’s surface. That figure must be used in the SB equation, producing a SB temperature of 360K. Dividing by four, and leaving out albedo influence gives you the 279K false value. The fact that the Earth averages 288K indicates it has cooling mechanisms at work. If you do the “divide by four” thingy, you are falling for the Warmists mantra. Any correlation with 279K (false value) and average ocean temperature is likely coincidental.

I must retire for the evening, and I see David has done so as well. But, just for the record, he left two questions unanswered:

1) Did he come up with the “divide by 4″ thingy all by himself? And, if he did not, where did he get the idea?

2) He stated that when he talked to PhD physicists, he was a “pretty bright guy”. I just wanted to know when he was NOT a “pretty bright guy”. (If he knows when he is “pretty bright”, he should know when he is not “pretty bright”, right?)

geran says:
November 16, 2013 at 7:27 pm
“The 1366 must be adjusted by albedo (0.3) to 956 because that is the actual flux reaching Earth’s surface. That figure must be used in the SB equation, producing a SB temperature of 360K. Dividing by four, and leaving out albedo influence gives you the 279K false value. The fact that the Earth averages 288K indicates it has cooling mechanisms at work. If you do the “divide by four” thingy, you are falling for the Warmists mantra. Any correlation with? 279K (false value) and average ocean temperature is likely coincidental.”

Respectfully, you’re way off here. The reason you are dividing by 4 is because of the geometry of the Earth and not because of some “Warmist” conspiracy. If the Earth was a flat disk you would be dividing by 2.

Rather than getting into a pointless back and forth though let me ask you 2 specific questions – What is the total Energy the Earth as a whole absorbs from the Sun and what is the surface area of the Earth?

The 1366 must be adjusted by albedo (0.3) to 956 because that is the actual flux reaching Earth’s surface. That figure must be used in the SB equation, producing a SB temperature of 360K. Dividing by four, and leaving out albedo influence gives you the 279K false value. The fact that the Earth averages 288K indicates it has cooling mechanisms at work. If you do the “divide by four” thingy, you are falling for the Warmists mantra. Any correlation with 279K (false value) and average ocean temperature is likely coincidental.
>>>>>>

Hmm, you can only get that 360K temp directly under the noonday Sun at the equator. It is not even an average temp of the earth, not to mention that it isn’t an equilibrium temperature and you can even get a higher temp than that there because the albedo is less there too.

Also albedo doesn’t matter if emission = absorption, albedo only affects the rate at which equilibrium is reached. And since the Sun has been roasting the Earth on a spit for 4.5 Billion years, equilibrium has long been reached.

Don’t discount the simple direct S-B approach too quickly. It almost completely eliminates the greenhouse affect. Remember the warmers claim it is 255K by some weird calculations that violate Kirchoffs Law.

That’s the textbook answer used by everyone from Thermoguys, to Astronomers, to Climate wonks. geran’s answer to you about albedo is spot on if you’re concerned about ocean temps at all.

@geran: I’ll drop this here before checking out in case you come across it. The 360k you calculate is correct only for solar noon on the plane of the ecliptic. As you note, that’s proper when starting with SB, rather than starting with unobtanium and then asking why SB doesn’t work. For the humor, the flux/4 value passed around in models works for solar noon ranging in latitudes from 52 degrees in the winter to 98 degrees in the summer. Yes, that 82 degrees latitude on the solar midnight side of things.

1) No, it’s the absolutely correct textbook answer for it. Do not pretend otherwise if you’re being graded.

2) I have absolutely no doubt he’s a pretty bright guy when talking to other people trained like he was. They all read the same books, devoured the same ideas, and speak the same shorthand. Speaking to people that don’t read the same books, have the same ideas, or speak the same shorthand always leads to friction in the best case. Doesn’t mean you can’t go have a beer afterwards. Hell, engineers will murder each other over thread counts on a screw and still hang out with cheer.

See – owe to Rich;
So if the Earth had no atmosphere and ocean and seasons and one treated each infinitesimal part of it as having separate temperature and radiation, what would be the mean temperature of the Earth?
>>>>>>>>>>>>>>>>>>

The moon has no (OK, almost no) atmosphere, no ocean, and with an inclination of only 1.5 degrees, almost no seasons. It gets nearly exactly the same insolation as does earth. So in theory it would make a good proxy to answer your question. Two problems. The first is that it has an albedo of only 0.11, while earth’s is about 0.3. The second is that the slow rotation of the moon combined with the lack of an atmosphere results in very large temperature swings. How you average them can change the number. Here is the diviner data:

Conventionally, the phrase “global warming” refers to an increase in the observed global average surface air temperature. This being the case, an increase in the global average surface air temperature along a linear trend line is not the “global warming.” Thus, it is not true that the global warming has paused. In your article, however, I find repeated implications that the global warming has paused. In particular:

* a NOAA report asserts that “an observed absence of warming of this duration is needed to create a discrepancy with the expected present-day warming rate” though a linear trend-line has a warming rate but the observed global surface air temperature does not,

* you state that “For those not too familiar with the ‘Pause’ in Earth’s warming…” though this “Pause” does not exist as an observable reality.

* you state that “In terms of exactly how long the ‘Pause’ has lasted, it depends on the data set and what it is being measured, e.g. in Werner Brozek’s recent article ‘Statistical Significances – How Long Is The Pause’? he showed that: 1. For GISS, the slope is flat since September 1, 2001 or 12 years, 1 month. (goes to September 30, 2013)” though this “slope” is the time rate of change of a linear trend line and is not the time rate of change of the observed global average surface air temperature,

* you state that “the Pause” is apparent in Earth’s atmospheric record…” but it is apparent only in unobserved global average surface air temperatures along a trend line.

* You state that “The Pause in ‘Earth’s Temperature’ appears in many of Earth’s observational records…” but fluctuations in the observed global average surface air temperature do not pause. It is only changes in non-observed and non-observable global average surface air temperatures along a linear trend line that pause. To summarize, “Earth’s Temperature” is a misnomer referring to a temperature along a linear trend-line and not to the temperature of the Earth.

I’m the Terry Oldberg who repeats a conclusion from the report entitled “An exploratory application of entropy minimax to weather prediction: estimating the likelihood of multi-year draughts in California.” OWRT Contract #14-34-001-8408. Entropy Limited. September 3, 1980. An abbreviated version of this report was published under peer-review by the American Meteorological Society.

In this research, patterns were discovered that made it possible to predict, over periods of between 1 and 3 years and with a statistical significance level of 96%, whether yearly precipitation would be wetter than or dryer than the median at specified precipitation gauges in the Sierra Nevada watershed east of Sacramento California. On the same data, the persistence hypothesis yielded a negligible significance level. The opening line of the Executive Summary of this report states that “Using the concept of entropy has given meteorologists, for the first time, the hope of statistically significant long range weather prediction.” In subsequent research, use of the concept of entropy yielded similar results in all of the far western states of the United States and in reference to global surface air temperatures as well as precipitation.

Jquip says:
November 16, 2013 at 4:54 pm
“Let me take it slowly then: Draw a line between the center of the Sun and the center of the Earth (Point A) and let the intersection of that line with the surface of the Earth be Point B. Then for any other point on the sunlit surface of Earth (Point C) we have the angle described by ABC. Let ABC be 60 degrees. Then if one unit square of sunlight is incident on a plane at that angle, it will fall on? 2 unit squares. Such that if the flux/m^2 is F then each unit square has F/2 flux/m^2 incident upon it. This is straight up obvious as stating F * Cosine(ABC). You may repeat this freely for any arbitrary point on the sunlight hemisphere.”

I’m sorry I’m really having a hard time following your point here. Doesn’t all this at the end of the day give the exact same numbers for the total solar energy absorbed by the Earth as the standard derivation? The area under a cosine curve as you described above is 2 which shows that the average flux hitting a flat disk is F the average hitting the side facing the sun is F/2 which is exactly what the purely geometric solution says.

Jquip at 4:54pm said:
“That is, the average height of the hemisphere of unit radius is the average value of the cosine of BAC for every possible C on that surface. That is your geometrically accurate model. And for our value F it gives 2F/3 as the average incident flux/m^2. Now find where the above is invalid.”

It is invalid because the value is F/2 as I shall demonstrate. I just don’t see how to make 2F/3 at all. In 2 dimensions, i.e. a semicircle (why isn’t it hemicircle?) instead of a hemisphere, the answer is 2F/pi, which is close to 2F/3 – but no cigar. In 3 dimensions, first drop a perpendicular from C (the general point on the surface) to AB, meeting at D, where A is the centre of the Earth and B is on the surface with the sun directly overhead. Letting the radius of the Earth be 1, then CD is sin t where t is the angle BAC. Now consider the annulus of all points C where the angle is between t and t+dt. This annulus has area 2 pi sin t dt, and the flux on this is cos t times as much. So the flux is 2 F pi sin t cos t dt and the area is 2 pi sin t dt. We now have to integrate each of these two quantities and then take the ratio, to get total flux divided by total surface area. This gives

“O H Dahlsveen;
I do suspect that you are using one of the editions of “Kiehl & Trenberth’s
>>>>>>>>>>>>>>>>> .
Your suspicions would be completely wrong”.
= = = = = = = = =
If my suspicions are completely wrong, which is – of course – very possible, then I am very interested to learn where you do get your numbers from. I am always willing to learn more. The only way to do that is to ask. – So, please tell.

Shawnhet says:
November 16, 2013 at 8:02 pm
Respectfully, you’re way off here. The reason you are dividing by 4 is because of the geometry of the Earth and not because of some “Warmist” conspiracy. If the Earth was a flat disk you would be dividing by 2.
>>>>>
Shawnhet, respectfully, you’re way off here. If the Earth were a flat disk, there would be no “dividing by 2”. An “ideal absorber” would indeed be a flat surface, and there is no “divide by 2” in the SB equation.

I think maybe you are trying to use the SB equation to find an “average”. You cannot do that because the equation is non-linear.

For your questions about Earth’s total energy and surface area, the values at wikipedia are close enough.

Genghis says:
November 16, 2013 at 8:03 pm
“Hmm, you can only get that 360K temp directly under the noonday Sun at the equator. It is not even an average temp of the earth, not to mention that it isn’t an equilibrium temperature and you can even get a higher temp than that there because the albedo is less there too.”
>>>>>
Genghis, be aware that the SB equation does not give you an “average temp”. At equilibrium it gives you an EXACT temp for the solar radiation.

“Also albedo doesn’t matter if emission = absorption, albedo only affects the rate at which equilibrium is reached. And since the Sun has been roasting the Earth on a spit for 4.5 Billion years, equilibrium has long been reached.”
>>>>>
Albedo DOES matter because it affects the amount of solar radiation reaching the Earth. You will not find 360K on the surface of the Earth due to the cooling mechanisms. Equilibrium has NOT been reached, nor is it likely to ever be reached, due to Earth’s rotation.

“Don’t discount the simple direct S-B approach too quickly. It almost completely eliminates the greenhouse affect. Remember the warmers claim it is 255K by some weird calculations that violate Kirchoffs Law.”
>>>>>

The “simple direct S-B approach” is to use the equation exactly as it is supposed to be used. Any other usage renders results invalid. Consequently, 255K and 279K are both invalid.

geran says:
November 17, 2013 at 5:10 am
“Genghis, be aware that the SB equation does not give you an “average temp”. At equilibrium it gives you an EXACT temp for the solar radiation.”
———
Yes, but because the Earth is rotating and the surface has mass that has to be warmed it is absorbing more radiation than it is emitting. Therefor it is not in equilibrium by definition. It isn’t even in a steady state.

“Also albedo doesn’t matter if emission = absorption, albedo only affects the rate at which equilibrium is reached. And since the Sun has been roasting the Earth on a spit for 4.5 Billion years, equilibrium has long been reached.”
>>>>>
Albedo DOES matter because it affects the amount of solar radiation reaching the Earth. You will not find 360K on the surface of the Earth due to the cooling mechanisms. Equilibrium has NOT been reached, nor is it likely to ever be reached, due to Earth’s rotation.
—————-
You are correct again, equilibrium for that particular spot or any particular spot is never reached and that is why 360K is never seen, but it has nothing to do with albedo or a cooling mechanism.

“Don’t discount the simple direct S-B approach too quickly. It almost completely eliminates the greenhouse affect. Remember the warmers claim it is 255K by some weird calculations that violate Kirchoffs Law.”
>>>>>
The “simple direct S-B approach” is to use the equation exactly as it is supposed to be used. Any other usage renders results invalid. Consequently, 255K and 279K are both invalid.
——–
I am using the S-B equation properly, by assuming equilibrium. It is the same 340 watts/m^2 Trenberth uses for the energy balance. The difference is that they claim that 30% of that number never gets absorbed. The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.

A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.

O H Dahlsveen;
If my suspicions are completely wrong, which is – of course – very possible, then I am very interested to learn where you do get your numbers from.
>>>>>>>>

I didn’t “get them” from anywhere. I learned how to apply SB Law in order to predict the temperature of components in a system during the design process for various pieces of equipment. For those applications the problem was considerably more complex. A current running through a resistor for example results in a certain amount of power (P in watts) being input to the resister. If I know the surface area of the resister, I ought to be able to calculated P in w/m2 and determine the temperature of the resister. Except that doesn’t work because the resister is also exposed to radiant energy from its local environment. So, I also need to know the average temperature of the immediate environment to calculate the base line temperature of the resister, and then calculate the amount the temperature of the resister will rise above the ambient temperature. But that number is also wrong because the resister is physically mounted in some manner to a circuit board or other apparatus, so there is going to be conduction between the resister and the apparatus. Now I need to also know the temperature of the apparatus under a range of conditions, and determine from there if conduction is going to increase, decrease, or not affect the temperature of the resister. With any luck the whole thing is inside a small closed container where the ambient temperature of the air rises to an equilibrium point during operation because it if isn’t, I then not only need to know the temperature of the air, but I have to calculate how much convection is going to be introduced during operation that will have a cooling effect beyond all the factors I’ve already listed. Plus that needs to be done across the operating temperature expected for the device in all use cases. For a control module in a car that could be sold anywhere in the world, I might have to do that set of calculations across a range of temperatures from -60C to +60C. With any luck the input voltage is DC. If it is AC, I’ll need to consider the frequency. For example, if the AC current is 60Hz, the average current would be zero. I’d use the RMS (root mean square) current instead to come up with an “effective average”. However, if the AC frequency is very low (say 1 Hz) and the temperature response of the component very rapid, that approximation would be invalid. I’d have to use peak voltage instead to determine maximum values.

Working out the math to come up with the effective black body temperature of earth is by comparison rather trivial.

geran says:
November 17, 2013 at 5:06 am
“Shawnhet, respectfully, you’re way off here. If the Earth were a flat disk, there would be no “dividing by 2”. An “ideal absorber” would indeed be a flat surface, and there is no “divide by 2” in the SB equation.”

You are right that there is no divide by 2 in the S-B equation – this comes from the fact that a disk(in this case) has a light side that at a given time absorbs light and dark side that does not. The dark side will still have a temperature though, and, thus, per S-B still emit energy to space. As such, you would treat a flat disk Earth as though it absorbed energy as though it was a single sided disk and *emitted* energy as though it was a double sided disk. Per S-B the temperature of an abject is determined by the amount of energy it emits, of course.

“I think maybe you are trying to use the SB equation to find an “average”. You cannot do that because the equation is non-linear.”

I am trying to find an average and I agree that the equation is non-linear but all your argument can do in this regard is *increase* the size of the apparent GHE, it does not decrease it or get you to a temperature of 360K that has to be cooled. As a hypothetical, imagine that through a network of mirrors or whatever most of the Energy hitting the Earth is focussed on a square kilometer of the Earth raising it to one million K. In order to energetically balance, the rest of the Earth’s temperature would have to be substantially less warm. If you were to take the average temperature calculated (by a comprehensive set of thermometers) on our hypothetical Earth and compare it to the calculated S-B one for our Earth the S-B must be higher (this is direct consequence of the non-linearity you mention).

The point here is that we can measure through our own set of thermometers that the average temp of the Earth’s surface is ~15C and what you mention above makes it impossible to return an answer above ~ -18C, we still have to explain where the 33C differential comes from. It can’t come from the non-linearity in S-B that would just increase the differential.

“For your questions about Earth’s total energy and surface area, the values at wikipedia are close enough.”

Cool. From the “energy budget of the Earth” page I get A. a total solar energy of 173 petawatts and B. From the main page on the Earth, i get a total surface area of the Earth of 5.1 X10^14 m^2 – by dividing A by B I get 339 W/m^2 which is pretty close to the 342 W/m^2 predicted under the standard derivation.

Genghis;The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.

Absorbed energy does work. Reflected energy does not. Hence absorbed and reflected are not exactly the same in an equilibrium or any other condition, and hence the logic behind removing reflected from the calculation,

A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.

You can’t predict the temperature of the ocean strictly from SB Law. You have to account for cooling via evaporation and convection. You also have to account for energy on a seasonal basis from sea ice melting and cooling. Then there’s rain. Then there’s wind from over land which may bring warmer or cooler air into contact with the ocean depending on any number of conditions. Evaporation and convective processes are the big ones though.

I notice that my reply to Jquip above from November 16, 2013 at 11:20 pm had some muddled language.

The sentence “The area under a cosine curve as you described above is 2 which shows that the average flux hitting a flat disk is F the average hitting the side facing the sun is F/2 which is exactly what the purely geometric solution says.” should read:(** denotes changes to previous).

The area under a cosine curve as you described above is 2 which shows that ** when** the average flux hitting a flat disk is F **per unit area** the average flux hitting the side **of a sphere** facing the sun is F/2 which is exactly what the purely geometric solution says.

@Shawnhet: “the average flux hitting a flat disk is F **per unit area** the average flux hitting the side **of a sphere”

Couple things. F is ‘watts per unit area’ already. You’re getting confused on ‘average.’ If we postulate a wall in space, perpendicular to the vector of the radiation, then F incident on the surface is identical to F projected at the surface. And as it is planar and perpendicular, then F anywhere is F everywhere. So we only need F projected at, but not on, and can plug it into SB and derive the temp anywhere and everywhere on that plane. But at which point the dimensions of the plane are completely meaningless.

@See – owe to Rich: “It is invalid because the value is…”

No, you didn’t show it was invalid. You produced a valid proof about a different subject. We are not talking about the total wattage incident on the circle describing the base of the hemisphere, nor of the area->area conversion. We are talking about the watts per unit area incident on the surface of the object. This is, beyond question, necessary as that’s the unit that SB takes and gives. And without question the Earth is not a wall in space.

This is a problem where reality is wrong or your model is. If you state that neither is wrong, then it is incumbent on you to show how you can reduce the geometry found in reality, to that of the preferred model you like, without introducing greater errors. This is, or should be, a remarkably trivial thing as it is a first business issue of modelling. For example, Newton or Gauss and the math that permits us to treat a spherical mass as a point mass. And if they had just said: “Imagine a cubic mass” therefore the average gravitational acceleration of a sphere is…” You’d be quite right in calling them charlatans. This is, of course, not what they did. They started with the geometry as found, and showed why and how it could be treated as a point mass.

davidmhoffer says:
November 17, 2013 at 8:55 am
Genghis;
The problem though and the error that they are making is that reflected is exactly the same as emitted in an equilibrium condition.

Absorbed energy does work. Reflected energy does not. Hence absorbed and reflected are not exactly the same in an equilibrium or any other condition, and hence the logic behind removing reflected from the calculation,
———–

That isn’t correct. A black object is exactly the same temperature as a white object in equilibrium and absorption = emission is exactly the same. Test it, I have.

Where albedo matters is in the time it takes to reach equilibrium. A black object will reach equilibrium very quickly while a highly reflective object will take a long time to reach equilibrium. The earth has had 4.5 billion years to reach equilibrium, time enough I think.

>>>>>>>>>>
A proof that they are wrong is the average temperature of the ocean, which is 6˚C (279K) or 340 Watts/M^2. Exactly the temperature predicted by the Stefan-Boltzman Law.

You can’t predict the temperature of the ocean strictly from SB Law. You have to account for cooling via evaporation and convection. You also have to account for energy on a seasonal basis from sea ice melting and cooling. Then there’s rain. Then there’s wind from over land which may bring warmer or cooler air into contact with the ocean depending on any number of conditions. Evaporation and convective processes are the big ones though.
————-

The processes you describe, evaporation, convection, conduction are energy flux within the system and do not effect the energy flow into or out of the system, only radiation can go into or out of the system. The Oceans contain over 90% of the total energy in the system so yes the S-B equation is a very good predictor of the oceans energy and temperature.

Jquip;
This is, beyond question, necessary as that’s the unit that SB takes and gives.
>>>>>>>>>>>>>>>

No it is not. SB Law is predicated on the energy absorbed by the object in joules per second being equal to the energy radiated in joules per second. Using w/m2 and the area of incidence is just a short cut to calculating the joules/s. The same goes for calculating the energy radiated. Using the total area times the w/m2 is just a short cut to determining the joules/s total.

Genghis: “Therefor it is not in equilibrium by definition. It isn’t even in a steady state.”

True, but as a first order issue we not only desire, but need, a fixed base to start from. One that allows us to reduce confounding factors in a *non destructive* manner. From which we can then add back in the confounding factors properly without making everything go loopy. There is, in this, a notion of dead-end trivia values. That is, output that is interesting for comparison between non-interacting objects, but which is so thoroughly bodgered, that we cannot use it for inputs to other models about that object. Which, if done, becomes the GIGO problem so commonly mentioned here about Climate folks using dead-end trivia values as input, to produce more dead-end trivia values.

” The difference is that they claim that 30% of that number never gets absorbed.”

This derives from albedo. The significant problem with the radiation budgets is that they posit the F/4 model as something other than a dead-end trivia value. Such that when that is then used as input, they then compare it to what the averaged measured temps are. (To the degree that this is advisable at all.) Quite unsurprisingly they get a difference between these to numbers. But as they have an absolute number for temp, and a simple difference between the two, then they back fill the difference with IR feedbacks. If you assume that none of the numbers are dead-end trivia, then it isn’t really relevant whether it’s IR feedback or not, it is necessary that there is feedback of some wavelengths.

The problem in this is that T derived from F/4 is not representative of any geometry or average at all. And further does not represent a manner similar to how the average measured temp is derived. So at the absolute beginning the difference between these numbers is a GIGO value; dead-end trivia. And so the IR feedbacks remain a GIGO problem. And it just continues to pile on from there.

davidmhoffer: “SB Law is predicated on the energy absorbed by the object in joules per second being equal to the energy radiated in joules per second.”

Yes, I’m perfectly aware of this. But that’s not at all the whole story is it? For if that were the case we could simply consider the total Joules on the cross section to be the Joules/m^2 for a single unit area. I hardly need point out how absurdly wrong that would be.

The sun emitts a flux which is measured as joules/s/m2 which is intercepted by a disk of radius R, and re-radiated by a sphere of the same radius R. The ratio of area of the disk to area of the sphere is 1/4. It is as simple as that.

davidmhoffer: “The sun emitts a flux which is measured as joules/s/m2 which is intercepted by a disk of radius R,”

Are the joules/s/m2 intercepted by the space-wall called Earth or the surface of the sphere called Earth? We’re done bargaining about unit areas, now we only need to finish bargaining about whether the Earth is flat or not.

Jquip says:
November 17, 2013 at 9:46 am
“Couple things. F is ‘watts per unit area’ already. You’re getting confused on ‘average.’ If we postulate a wall in space, perpendicular to the vector of the radiation, then F incident on the surface is identical to F projected at the surface. And as it is planar and perpendicular, then F anywhere is F everywhere. So we only need F projected at, but not on, and can plug it into SB and derive the temp anywhere and everywhere on that plane. But at which point the dimensions of the plane are completely meaningless.”

Respectfully, you are avoiding the issue I raised. You provided a framework such the solar flux incident at point C on the surface of the Earth was Fcos(BAC). This is perfectly valid but not very useful on its own and leads to the next obvious question: what does the framework that you provided us tell us about the average flux at the surface of the Earth?

I submit that your framework leads to the exact same answer for the average value or F from the surface of the Earth as the standard derivation (and I have provided math to back that up). If I am mistaken somehow, please tell me what the correct (per you) answer is and how you calculate it.

Honestly, I don’t see how you get from there from here; so there’s not any manner in which I think I can properly address it to begin with. I understand you’re after a cosine curve, but I can’t fathom how you get from the average height of a hemisphere to the area under a cosine curve. If my notes didn’t clear things up for you, then you’ll need to clear things up for me :P

As for the ‘same value’ on standard deviations: My only assumption here is that you intend to mean from -1 to +1 sd, which is certainly not the same as 2/3. As for what it tells us? That every average is valid for every data set, so long as your error bars are large enough and you’re not concerned if it’s useful for later modeling tasks. Since you mention statistics, simply take the average of a bimodal distribution and then see what you can claim as valid and accurate information that gives you about the distribution itself.

Specifically here, we’re using one arbitrary manner of producing an average flux to produce an arbitrary temperature. And in the other we’re using an average temperature to produce an arbitrary flux. But, for bonus points, the average flux used to derive the arbitrary temperature is based on an a priori model of self-contradictory conditions (In the use we’re trying to put it to) to justify an average flux from an arbitrary temperature. Which is a terribly tangled bit of circular nonsense and a bit hard to sort through. So apologies for that, but it wasn’t my creation.

What I’ve put forward here is little more than how actual photons hit an actual sphere. The average flux of which can be used to derive T. But if you’re interested in radiation budgets and the average T as measured on the surface, then it should be done as the intergration of T, rather than the flux. That computes both things in the same manner. So while there are always errors, both values are computed in the same manner. So we can state that, whatever the error is in these calculations, it is only one rather than a collection of them going goodness which directions.

davidmhoffer: “The cross section of the energy flux intercepted by the earth is flat. The earth is a sphere.”

So since we’re all certain that the flux is intercepted by the surface of the Round Earth, then if the F/2 calculation for the lit side is correct then there is a proof that we can reduce 2F/3 to it. This is not a bit of vulgarity or asking too much of people producing physical models. And, as noted, is precisely the same thing that was done in justifying the ability to treat spherical masses as point masses.

There is no necessity that using global equilibrium on a volumetric body, or on a differentially irradiated body makes anything that is feasible, non-absurd, or violates other laws of physics. But if that cannot be shown, then we are attempting to use a theoretically model — an analogy — in a manner that stretches it beyond the breaking point. But if we are to state that it is perfectly cromulent, then there is a proof of it that we do not get absurd results. And all we need for that is the reduction from what actually occurs in reality as 2F/3 to the conceptual notion of a the area of a hemisphere in relation to a disc as F/2.

If Thermo has it’s big boy pants on, and the use of this by Astronomers, Cosmologists, and Climatologists isn’t violating Thermo and the rest of the laws of physics then: Such a proof exists.

jquip;
So since we’re all certain that the flux is intercepted by the surface of the Round Earth, then if the F/2 calculation for the lit side is correct then there is a proof that we can reduce 2F/3 to it.
>>>>>>>>>>

sigh.
There is no 2F and there is no 3. If you agree that the lit side is F/2 then for the sphere as a whole F remains the same and the lit side plus the dark side comes to 4. Which gives you F/4.

davidmhoffer: “He got F/2 for a hemisphere which is exactly the same as F/4 for the sphere.”

Oh? Then the proof I gave of the average height of a hemisphere is invalid and you can show where it went astray. You may do so now. Hint: If, at any point, you could have you would have. Your position is not one of an honest man.

“If you agree that the lit side is F/2 then for the sphere as a whole F remains the same and the lit side plus the dark side comes to 4. ”

If you agree the Earth is round and photons are incident on it, then you agree that the value is 2F/3 for the lit side. In naive average over the sphere that would be F/3.

But at this point should we both agree that there is no proof that reduces the absolutely obvious and pedestrian geometry involved to a condition where we may treat things as if it were a Flat Earth? For if not, then certainly you have such a proof.

The problem here is that you keep agreeing with the 10th grade geometry I’m presenting to you. And indeed it would be ludicrous for you to deny it. But you keep prevaricating about how to get from what unquestionably is to the so far unprovable what you want it be. Which is common nonsense easily found, but still nonsense. It’s magical thinking of the first order.

Upthread a self described mathematician has lamented the need to explain the reason to divide by 4 at all. I’ve explained it using simple geometry. Shawnhet has explained the math and shown that it matches precisely the geometry. You’ve admitted that for the lit side it is F/2, the only logical consequence of which is that for the sphere as a whole, F remains the same and area doubles, giving F/4.

Jquip says:
November 17, 2013 at 11:55 am
“Honestly, I don’t see how you get from there from here; so there’s not any manner in which I think I can properly address it to begin with. I understand you’re after a cosine curve, but I can’t fathom how you get from the average height of a hemisphere to the area under a cosine curve. If my notes didn’t clear things up for you, then you’ll need to clear things up for me :P”

Ok, I can see my area under a cosine curve was more of a help than a hindrance. Suffice it to say, that there is nothing at the end of the day about your FcosBAC framework that would produce a difference for the average than the standard deviation.

“What I’ve put forward here is little more than how actual photons hit an actual sphere. The average flux of which can be used to derive T”

Then, why don’t you derive it? You’ve got your FcosBAC framework that is according to you different from the standard one. It seems to me that your whole approach is based on not being able to calculate the average flux at all. If that is the case, all you are left with is your intuition that the standard derivation is wrong.

Working out the math to come up with the effective black body temperature of earth is by comparison rather trivial.”

= = = = = = = = == =

Thank you very much for that info “davidmhoffer” I shall print your comment off and learn it, But right now all I can say is that I do have a lot of respect for guys who have “deep or comprehensive knowledge” in the fields of electrics and/or electronics.

For that reason alone I am puzzled as to why you can say: “Working out the math to come up with the effective black body temperature of earth is by comparison rather trivial.”

Yes, maybe it is “trivial” – providing you have got all the right numbers at your disposal, but if you are ignoring “important facts” – two of which are that the Earth is not a true “Black Body” and second, – maybe more importantly; The Earth rotates around its own axis one full turn every 24 hours.

So, IMHO to divide the so called “Solar Constant by 4, is the same as taking a “snapshot” of the Earth in orbit. Fine if you want to find out the “Average Solar Irradiation” for any given second of the day, but useless for anything else. Therefore the ‘numbers’ in your calculus is ‘somewhat lacking’.

The thing not to overlook is that at every second of every day it is 12 o’clock noon somewhere along the Equator – and along the same “vertical line” from pole to pole. Therefore, my friend, the Earth always receives the “FULL WACK” of solar power 24/7.

I know, – there are the hours of no solar irradiation that poke a stick into the spokes of that wheel. – Well not really, because – one theory that may well be correct – says that soon after the solar energy input stops along that said “vertical line” i.e. at night-time, air-convection also stops. The air “collapses in on it-self” (becomes “Down-Welling”) thus it becomes denser and less room is left between the H2O, and also between other GHGas molecules if you like, and the IR energy has greater difficulties in escaping to space.

If you have your cork, toothpick and ball and you give the ball a complete turn before removing it you will find groves instead of small indentations.

Yapyapyap. If this is so, you can show where my example went astray. What an honest and knowledgable man does in refutation, is refute. What you have done is continually change your mind about the flat Earth theory. Put up or shut up.

@Shawnhet: “Suffice it to say, that there is nothing at the end of the day about your FcosBAC framework that would produce a difference for the average than the standard deviation.”

Oh? Then show the derivation from one to the other. As you say you can do it, present the math for it. Rather than make yourself a fool with a naked assertion, show me a fool with an argument. As said already, I don’t see how you’re doing it. If you don’t see how you’re doing it either, then we’re both lost and nothing has been shown.

“Then, why don’t you derive it?”

See my post at: November 16, 2013 at 4:54 pm. It’s already been explained. Either you can show how that is invalid, or it has indeed been derived.

O H Dahlsveen;
So, IMHO to divide the so called “Solar Constant by 4, is the same as taking a “snapshot” of the Earth in orbit. Fine if you want to find out the “Average Solar Irradiation” for any given second of the day, but useless for anything else. Therefore the ‘numbers’ in your calculus is ‘somewhat lacking’.
>>>>>>>>>>>>>>>>

You are correct. SB Law does no more than that. There are considerable problems with SB Law in terms of understanding the “temperature” of an oblate sphere rotating in space every 24 hours at a 20+ degree inclination in an elliptical orbit. I’m happy to discuss those problems, but there is little value in doing so when the basic application of SB Law is not understood. Once you understand the reason to divide by 4 and accept that it is in fact a proper application of SB Law to do so, we can move onto other issues.

The following is a discussion of the utter madness of calculating a temperature anomaly for the earth as a whole from station data. I wrote it to be an easy read, and most of what is in it applies equally to the mind boggling stupidity of trying to average temperatures as well as you can demonstrate that it is possible to arrive at a lower average temperature on a surface that has gained energy and vice versa.

Despite his criticisms of 255K as a baseline, Dr Brown has since used that number frequently in discussion because although it is a terrible baseline, the SB Law calculation done properly delivers that value, and so it is of value for general discussion. A more accurate way of calculating a baseline temperature was proposed by Nikolov and Zeller, a methodology that I actually supported, but alas they made really major errors in the rest of their physics and the baby got thrown out with the bath water.

“Oh? Then show the derivation from one to the other. As you say you can do it, present the math for it. Rather than make yourself a fool with a naked assertion, show me a fool with an argument. As said already, I don’t see how you’re doing it. If you don’t see how you’re doing it either, then we’re both lost and nothing has been shown.”

Well, you are actually asking quite a bit here so I’m just going to point the way not walk you through every single step. Luckily I have been able to find something on youtube that directly speaks to this – from the above, the average value of a cosine is 2/pi over the 180 degree arc we are looking at. Frankly, I was trying to keep things simple because actually, to calculate all the points on a (hemi)sphere, you need two angles not one(one each for longitude and latitude). Since you don’t really dispute the ratio of the surface area of the Earth to an Earth-sized disk, I am not sure what we are even talking about.

“See my post at: November 16, 2013 at 4:54 pm. It’s already been explained. Either you can show how that is invalid, or it has indeed been derived.”

What is your average T? You never calculate that you just mention that 2F/3 (which is just a close approximation of my number above). To get the actually correct number you will need to add the second angle.

In any case, if you think that every point in a sphere emits 2F/3 of what it receives – you have just discovered free energy. Just take a flashlight a with a flux of F on a circle the size of a tennis ball on the wall, then take the wall down and replace it with a suspended tennis ball. Guess what, you have increased the total energy by 50%(actually 57%)!!

Awesome goalpost moving and nice try pushing the burden off on Shawnhet. But now your claim is that the math Shawnhet hasn’t shown shows the same thing as the math you haven’t shown either. But as you so certainly know both then it remains that you can show either or both. And neither has been shown at all. The only thing you continue to produce is dishonesty. And don’t take that badly at all, I wish I got paid to study the climate as well.

Yes, I know the bit about what the area under a sinusoid is. The problem is how that relates to what we’re talking about. And, separately, how a gaussian distribution does. For that latter, the nearest I can figure is that you assume the distribution provided in my example is a normal distribution; which it is not. But if I take that idea, then I can’t figure out why you think the standard deviation has anything to do with it.

“To get the actually correct number you will need to add the second angle.”

This is probably the sticker then. The average flux being 2F/3 for the lit side, or F/3 for the whole. But 2F/3 is not the single angle. The single angle is just to demonstrate the geometry involved and it’s relation to the height of a hemisphere. eg. On a unit radius the height of a hemisphere at any single point is cos BAC. The incident flux at that same point is F * cos BAC. So it follows that the average incident flux is the average attenuation of F times F; and so the average height of the hemisphere. Draw it out on a page, it helps a lot. But the average height of a unit hemisphere is 2/3, and so the average incident flux is 2F/3 over that hemisphere. As the unlit has no incident radiation by the model, then F/3 for the average whole.

Taking temp from flux, no matter how good or bad the average, is then standard. But by caveat and consideration we need assume no more than that each point as F * cos BAC radiates then same as a consideration of local equilibrium. There’s lots of fun arguments with that which aren’t interesting until the geometry portion is understood.

Oops, I got confused on the last bit above. His approach does not add energy, it is just a reasonably good approximation of my 2/pi number above.

The rest of my post stands (and for those who wish to consider it further) I believe that the precise function that will lead to the correct ratio of the surface flux absorbed by a hemisphere is the integral of cos^2 x over the interval of -pi/2 to pi/2 divided by pi(the length of the interval).

I just can’t figure out a simple to lay it out mathematically that won’t take a half an hour. A quick and dirty double check is to take numbers from a trig table for the Cosine from one to ninety degrees and square them, then take the average of all the squares. The average of that is ~0.5. The correct interpretation of that number is that given a (flat) circle that recieves F in flux on each of its points a hemisphere of the same radius where the flux at any point is given by Jquip’s FcosBAC placed on top of that circle – all the points on that hemisphere will have an average flux of 0.5F.

There are many ways to show this but they all come up with the same answer.

Jquip, before you dig yourself in too far you do need to reconsider your claims of 2F/3. This is exactly related to the mean temperature of a mass-less Earth with no thermal inertia involved brought up by Nikolov and Zeller and I have numerically integrated it four different ways, others have also checked the math, even Joel Shores found it also correct I believe, 154.3 K mean temperature meaning the true GHE is not 33°C as held by most climatologists but ≈134°C.

Now what you are questioning is the mean point-wise flux, cosine angle and area weight adjusted, a every point on this globe and if you will follow I have to first calculate that to even get to the mean temperature, that 154.3 K using an emissivity of 0.955 and na albedo of 0.12. So I went back into those integration programs and added the two lines to also accumulate and then mean the flux across the globe and it is not 2F/3, it is 340.5 W/m² when the TSI is 1362 W/m² or one fourth. Someone above was trying to queue you to the fact what you are proposing greatly affects mean temperatures but no mean fluxes, point-wise.

You can integrate this by Monte Carlo of randomly but evenly distribute points over the Earth’s surface, cosine and area adjusted of course. or you can take a polar view and integrate per concentric latitude bands, or you can take a mathematically harder computation to take a view over the equator at Greenwich meridian and do just the lit hemisphere per also latitude of tiny bands, any way you get 340.5 W/m² mean flux and 154.3 K described above as the mean temperature on the printouts. If I were you I would stop insisting on something not correct but instead look into why all mean temperature computations using such a mean of flat-earth flux and not point-wise on a sphere are in fact all incorrect and are very misleading.

In fact if you then integrate, same program with different parameters, use 0.30 for the albedo and 0.986 for the emissivity, same TSI, you get 144.55 K which is exactly one-half of the 289.1 K claimed in Trenberth et al’s last paper. If you think deep on that one you should see what I see, a totally opaque and isotropic ‘reflecting’ atmosphere exactly doubles the, get this, the temperature, and THAT is what makes us that huge GHE of greater than 134K since the albedo also changed between those two cases mentioned! I find that so, what to say… illuminating!

If you don’t want to numerically integrate, N&K’s poster/paper has the closed form equation that will feed those same numbers out I mentioned above but much simpler. Guess not many have delved as deep as I into some of these relationships for I’ve been waiting and the same never appears.

Just point of information here, when I say standard derivation I mean the standard derivation of the blackbody temperature of the Earth ie 255K using standard geometric reasoning.

“The incident flux at that same point is F * cos BAC. So it follows that the average incident flux is the average attenuation of F times F; and so the average height of the hemisphere. Draw it out on a page, it helps a lot. But the average height of a unit hemisphere is 2/3, and so the average incident flux is 2F/3 over that hemisphere. As the unlit has no incident radiation by the model, then F/3 for the average whole.”

Since I don’t see this getting resolved any other way -let me get precise here. Your expression F*Cos BAC only describes the values of F along a single line of latitute or longitude. The actual description of the flux at every point of the Earth’s surface is F* Cos BAC * CosDAC – one of each for latitude and longitude. (You are not multiplying the Flux by the attenuation of itself
(that would give you Watts squared as units.) As such, you are looking for the average value of a cos^2 function (or in your terms (2//3)^2 instead of 2/3. The actual number is 0.5 but an easy way of showing that derivation is escaping me at the moment. In my post above this one, I mentioned a quick and dirty way of (using trig tables) going from the cos^2 relationship like you hint at to the average flux values. The correct value is ~0.5F for the lit side of the Earth as compared to a flat disk the size of the Earth getting an average of F.

If you define your coordinates in that manner. If you describe the light as intersecting the pole, then Cos BAC is the latitude. Or, as mentioned in the integral for the surface of a hemisphere by the other fellow, an annular ring. It need not be the actual pole that the sphere revolves around, or anything else; it’s just a reference point until we start getting into grey body considerations.

wayne: “If you don’t want to numerically integrate, N&K’s poster/paper has the closed form equation that will feed those same numbers out I mentioned above but much simpler. ”

Oho! I gave up on it before I got to a closed form. As I mentioned earlier, it was ages ago and all three manners come up with significantly different numbers. The 154.3K you mention strikes my memory as absurdly low, but I’ll grant you’re probably right. Deriving T from average flux was much higher than integrating over T, in the same geometric model, to get the average. And thanks for the heads up on N&K, I’ll see if I can turn it up in google.

The question isn’t whether it seems absurd or not, it is whether or not it is an accurate base to start from. That is, is it in the realm of physical laws and geometry or not. As moving away from a black body consideration we then need albedo, conductivity, atmosphere, daylight (and nightime…) and all the other things that slow down absorption and emission both. A take away point about pulling averages off any non-linear description is that it is meaningless and unstable unless you take account of just what sort of non-linearity it is. Standard distributions being not just the gold-standard here, but about the only intelligible place to take an average given its properties and symmetry.

But the convenience with F/4 is that it is close as a postulated airless black body light bulb system to the system we have: An atmosphere covered grey body orbiting its radiation source. But that’s right up there with correlation is not causation in that happy accidents mean very little. For dealing with surface features and climate, it is simply irresponsible to start from the F/4 consideration in every case. As to use it properly, as a global equilibrium case, requires embedding the sun inside the Earth or vice versa. And if we had that, it would be perfect for use. We’d also never need streetlamps, which would save on CO2 production. >->

Jquip, you have some catch up to do since you brought up the though that this is not a flat disk, the Earth is not evenly illuminated, the math all seems wrong. I agree and I now know it is all wrong but for you to understand what I was saying you probably need to read something. Nikolov and Zeller’s ‘Unified Theory of Climate’ was not swallowed well here and I agree it was not complete especially near the end. See this or just search using this site’s search box for ‘Nikolov’.

I was just intregued by their work right at the first of their paper and it addresses exactly what you raised here. Yes, it takes a view more like the moon’s albedo and emissivity and doesn’t allow for any thermal inertia in the soil but it shines some light on that the 33°C ‘greehouse effect’ compared to an Earth without infrared active gases is far, far too low. Yes, you should look into that area of history here, since you are questioning the geometry and the solar radiation you should enjoy the read (there are thousands of comments in multiple posts on their poster/paper)

wayne: “I agree and I now know it is all wrong but for you to understand what I was saying you probably need to read something.”

Ah, beauty; thanks for the link. And yes, we’re all on the same page. Except that: I disagree with the statement at the think “our atmosphere boosts Earth’s surface temperature not by 18K—33K as currently assumed, but by 133K!”. Forgive if I state things you don’t need stated: Specifically, a large misunderstanding about black-body temperatures are that they are not simply ideal, but the coldest possible because they are ideal. And in any condition where emissivity is > 1 – albedo, then the same condition holds in absence of thermal inertia; as less the correction for albedo it functions like a black body. So the bulk of anything we can dream of will have a temperature strictly higher than the black body ideal for no more reason than it isn’t a black body. And that remains true if we do the standard black body construction of an infinitely thin surface backed by a magic mirror.

Such things are why I harp on an accurate base to work from. Which we obviously don’t have;and there’s hardly a reason to shoot in the dark when we don’t have to.

wayne;
I was just intregued by their work right at the first of their paper
>>>>>>>>>>>>>>>>.

Yeah, me to. Too bad they screwed it up so bad in the end that the thing got dismissed in its entirety. That said, I got into some private discussions with a number of physicists. I think it was Joel Shore that pointed out to me that SB Law is still relevant even in an N&Z model. In their model, the larger the temperature swings you deal with (seasonal, latitude, daily) the “colder” an average temperature you get. Conversely, the more uniform the temperature is, the “warmer” an average temperature you arrive at, and the limit you approach as the temperature variance approaches zero is the SB Law value. So SB Law still winds up defining the maximum temperature the surface can be at sans greenhouse effect. But we’d still be WAY better off trending average of fourth root of T rather than T to quantify any energy imbalance that may or may not exist.

Jquip says:
November 17, 2013 at 5:04 pm
“Shawnet: “one of each for latitude and longitude. ”
If you define your coordinates in that manner. If you describe the light as intersecting the pole, then Cos BAC is the latitude. Or, as mentioned in the integral for the surface of a hemisphere by the other fellow, an annular ring. It need not be the actual pole that the sphere revolves around, or anything else; it’s just a reference point until we start getting into grey body considerations.”

You need to have two angles to describe the complete surface of the Earth, there is no way around it. Think about it this way – how much F does a point P1 on the equator get if it is high noon and how much did it get 4 hours before noon. Now how much does point P2 that is directly North of P1 but on the Arctic circle get 4 hours before noon. You can’t describe P1- noon, and P1 noon-4, P2 noon and P2 noon-4 using one angle and if your equation can’t describe the entire surface of the Earth, then obviously it can’t calculate an accurate average F over the entire surface of the Earth.

I had missed the earlier reply to you from See owe to Rich dealing with the annular ring – this was an elegant way of calculating the relationship of average F on the surface to what a hypothetical disk average should be.

At the end of the day, your calculation of 2F/3 is only valid for two small sections of the Earth (directly along the line of the equator and directly along the line of high noon.

As geran points out, due to the rotation of Earth on its axis (among other causes), an equilibrium temperature is never reached on Earth. A consequence is for the equilibrium temperature to be unobservable.

It follows from the unobservability that quantities which are functions of the equilibrium temperature, including the equilibrium climate sensitivity (TECS), do not exist as scientific concepts. By building TECS into the foundation of their discipline, climatologists have ensured that their discipline is a pseudo-science. A science of climate must be built upon observables, including temperature but not including the equilibrium temperature..

Shawnhet;
At the end of the day, your calculation of 2F/3 is only valid for two small sections of the Earth (directly along the line of the equator and directly along the line of high noon.
>>>>>>>>>>>>>>>>

Not to mention that if correct it would falsify all of Euclidean geometry.

this reduces to pi/4 divided by pi/2 which gives us an average value of cos2 x over the interval of pi/2 and 0 of 0.5. Subbing this into Jquip’s F *cosBAC*cosBAD framework gives an average value of the Flux on the sunward side of a hemisphere of 0.5F where F is the Flux that a flat disk receives on a point on its surface.

Well thanks for doing the heavy lifting, I suspect that Jquip would not be persuaded by anything less than a mathematical proof. One of the things I learned from studying Einstein’s work was the importance of two things:

1) if you cannot first visualize the problem, you cannot solve it mathematically (except perhaps by luck).
2) keep everything as simple as possible, but no simpler

The simplest way to approach this problem is straight geometry. Area of a sphere verses the area of a disk of the same radius yields a ratio of 4:1 (or for a hemisphere per your math above, 1:2) It is as simple as that. I just couldn’t see the value of getting deep into the math when the only possible answer had to match the geometry. The other trick I learned a long time ago however was to come up with two solutions to the same problem. If you get different answers, one or both are wrong. If you get the same answer, it doesn’t mean with 100% certainty you are right, just you are more likely to be right. One of my first year math classes there was a project to predict the temperature of a bottle of beer sitting in a cold stream at any given point in time based on just two measurements in time. The class as a whole found about 4 different ways of doing it, and upon experimentation, they were all wrong by the same amount as they had all made the same mistake, which was to ignore conductance between the stream bed and the bottom of the bottle.

Confused Photon, please explain, in detail, what makes this a Mickey Mouse analysis. Did you have trouble understanding it? Do you have a legitimate grievance with the overall content, a specific analysis in the presentation or are you resorting to name calling because you don’t agree but don’t have a valid complaint?
If only the billions of dollars of research over the past three decades had resulted in some empirical, scientific evidence that the earth was actually warming incontrollably and that CO2 and man were responsible then all these horrible deniers would probably go away. Imagine the nerve of people who demand evidence before adopting a position.
You may go ahead and call me names now. That will convince people to see things your way. I know your statement ceertainly made me reassess my position. I now see the folly of wanting to have facts and legitimate supporting evidence before making a decision. Thanks for showing me that by simply belittling others without any evidence we nullify the validity of their work.